Direct imaging of exoplanets is able to measure planetary mass, orbital parameters and other critical physical information, which can support investigations into the potential processes behind the formation and evolution of both solar and extrasolar planetary systems. However, due to the significant brightness contrast ratio between exoplanets and their host stars, as well as limitations imposed by telescope apertures, the faint planetary signals are often obscured by the diffraction light from thire host star. Furthermore, many current and planned large-aperture astronomical telescopes adopt segmented mirror structures, the gaps between adjacent mirror segments will lead to considerable additional diffraction, thus it poses even greater challenges to the direct imaging studies of exoplanets.To address this issue, a high-contrast imaging coronagraph system based on pupil phase modulation by using a large-actuator-number and high stability Spatial Light Modulator (SLM) is proposed in this paper. The system aims to achieve high-contrast imaging capability across the 360° full-field region for telescopes with a monolithic mirror and large-aperture segmented mirrors. The Stochastic Parallel Gradient Descent (SPGD) optimization algorithm is employed to control the SLM for pupil phase optimization, and the contrast performance is evaluated using an objective function defined from the Point Spread Function (PSF) images collected by a CCD. Firstly, the fundamental principles of pupil phase modulation and the SPGD algorithm are introduced, theoretically demonstrating the feasibility of using SPGD to control the SLM for optimizing the pupil phase distribution to achieve high-contrast dark zones. Based on practical observation targets, the inner and outer working angles of the coronagraph system are defined as four times the working wavelength divided by the telescope aperture and twelve times the working wavelength divided by the telescope aperture, respectively, which further determines the evaluation function of the optimization algorithm. Secondly, an optimization testing system for a phase modulation-based coronagraph is constructed, in which a phase-type SLM is used to modulate the pupil plane phase, moreover, an amplitude-type SLM is used to simulate the pupil structure of large astronomical telescopes, enabling optimized design and experimental tests for both monolithic and segmented-mirror telescopes with ten meters aperture or larger. In the experiment, to fully leverage the advantage of the large number of actuators on the SLM and ensure rapid convergence of the SPGD algorithm for optimal imaging contrast performance, a finite-band ring-based pupil phase modulation method is designed. This method distributes a finite number of equally wide concentric rings from the center of the pupil along the radial direction, assigning the same phase value to each ring to reduce phase precision while maintaining final imaging contrast performance, and the modulated pupil area matches or slightly exceeds the simulated telescope pupil to maintain modulation effectiveness. Voltages of actuators in each ring within the SLM's optimization region are controlled by using an SPGD optimization algorithm that adjusts the pupil phase values according to the values of the objective function to improve contrast performance. The optimal imaging contrast on the focal plane in the experiment is eventually achieved when the objective function's value no longer decreases and reaches the minimum. Optimization tests are conducted for simulated monolithic and segmented-mirror telescopes individually by using an amplitude-modulated SLM to simulate the pupil of each configuration. PSF images before and after modulation are compared and significant modulation effects can be observed. The final optimized pupil distribution is acquired, and the imaging contrast curve is measured using the triple-exposure method developed by our group. To eliminate uncertainties caused by curve-fitting errors in the contrast measurement, an additional laser source was used to simulate a planetary light source for further verification of the system's imaging contrast. Finally, we conduct an analysis and discussion based on the results. The experimental results show that the proposed high-contrast imaging system achieved an imaging contrast of approximately 3.6×10^-6 after 5 000 iterations for a simulated monolithic mirror telescope, while for the simulated large-aperture telescope with segmented mirrors, an imaging contrast of approximately 9.3×10^-6 was achieved after 9 400 iterations of optimization. By comparing the two outcomes of the imaging contrast, it indicates that the complex additional diffraction caused by the gaps between adjacent segments in a large-aperture telescope with segmented mirrors sacrifices a portion of the coronagraph system's imaging contrast performance, posing challenges for high-contrast imaging in coronagraph systems and needs to be carefully tackled.In conclusion, the proposed high-contrast imaging coronagraph system based on a phase-modulation SLM achieved an imaging contrast better than 10^-5 within the 360° full-field range of 4λ/D to 12λ/D from the PSF center in optimization tests simulating both monolithic and large-aperture telescopes with segmented mirrors. The proposed phase-modulation coronagraph system shows potential for direct imaging of exoplanets.