Computed tomography imaging spectroscopy (CTIS) has the ability of traditional imaging spectrometers to acquire two-dimensional images and one-dimensional spectra of the target space. It also has the characteristics of high-throughput measurement and non-scanning imaging, which has a wider range of applications in the field of spectral imaging. According to the Center Slice Theorem, the performance of the CTIS is mainly restricted by the performance of the Focal Plane Array(FPA) and the two-dimensional dispersive element. The previous research mainly focused on improving the design of the two-dimensional dispersive element to increase the diffraction order and projection angle to enhance the sampling and spectral accuracy. This paper focused on the FPA two-dimension dispersion projection measurement. It proposed a method of combining parallel block-compressed sensing and CTIS to establish block-compressed sensing computed tomography imaging spectroscopy (BCSCTIS) model, which uses the low-resolution FPA to achieve the measurement of the high-resolution dispersive projection and further achieves the performance higher than traditional direct computed-tomography measurement. In order to verify the correctness and feasibility of the BCSCTIS model, this paper carried out a BCSCTIS simulation experiment and carried out the corresponding optical system experiment in turn. The system matrix from a three-dimensional spectral cube to a two-dimensional dispersion projection was simulated in the simulation experiment. The hyperspectral data set was used to quantitatively compare the reconstruction results of the direct measurement model of dispersion projection with the that parallel block compressed sensing measurement model, and the results showed parallel block compressed sensing computed tomography imaging spectroscopy can obtain higher spectral reconstruction quality. It can achieve a significant improvement in spectral projection acquisition resolution and spectral reconstruction quality higher than the performance of FPA itself. Furthermore, the CTIS optical experimental data were processed by parallel block compressed sensing, and the effectiveness and feasibility of BCSCTIS were further verified. In the optical experiment, the system matrix was accurately calibrated point-by-point using a supercontinuum and a reflective digital micro-mirror device (DMD). Also a parallel calibration method to improve the calibration efficiency was proposed. In the experiment, the calibration time is reduced to one-fourth of the single-point calibration. The conclusion is consistent with the simulation experiment, which further confirms the correctness and feasibility of the proposed BCSCTIS.