In space gravitational wave detection, the telescope is an important part of the space laser interferometry system. The wavefront error at the exit pupil of the telescope is coupled with the Tilt-To-Length (TTL) noise, which becomes the main source of noise in space gravitational wave detection. Firstly, based on the interference model between a flat-top beam and a Gaussian beam, the Fringe Zernike polynomial is used to characterize the wavefront error at the exit pupil of the telescope, and the LISA Pathfinder (LPF) signal is used to analyze the coupling mechanism of the wavefront error at the exit pupil and the TTL noise. Secondly, the Monte Carlo analysis method is used to study the influence of the proportion of low-order aberrations on the TTL coupling noise under different numerical wavefront errors, and determine the low-order aberration proportions which meets the requirements of TTL coupling noise control at the exit pupil in the design of the telescope optical system under different numerical wavefront errors. Finally, based on the above theoretical analysis results and the aberration control requirements, the optical design of the space gravitational wave detection telescope is completed. The diameter of the entrance pupil of the telescope is 200 mm, and the RMS value of the wavefront error at the exit pupil is 0.01908λ. The proportion of low-order aberrations is not higher than 50%. The analysis results show that the TTL coupling noise does not exceed 8.25 pm/μrad when the beam jitter is within ±300 μrad. Through tolerance analysis, the maximum TTL coupling noise is determined to be 15.50 pm/μrad, which meets the requirements of space gravitational wave detection.