In the Taiji Program, the space gravitational wave (GW) telescope is an important component of the space laser interferometer, which is used to receive and transmit laser signals, and has strict requirements in terms of light intensity signals and tilt-to-length (TTL) noise. Therefore, the telescope has a particular design; it should have a large aperture to meet the demand for light intensity signals, and the TTL coupling noise should be suppressed in the design process. Based on the primary aberration theory, the solution of the four-mirror off-axis initial structure is described. According to the interference model of flat-topped and Gaussian beams, the coupling coefficient of wavefront error and TTL noise at the exit pupil of the telescope are analytically calculated using the average phase signal. The optimization method and design flow are established, considering the special requirements of the space GW telescope. The results indicate that the diameter of the telescope entrance pupil is 400 mm, and the system magnification is 80 × . The root mean square (RMS) value of wavefront errors is better than 0.00504 λ (λ = 1064 nm) within ±8 μrad of the scientific field of view, and the coupling coefficient is not more than 1.7 pm / μrad within ±600 μrad of jitter angle. The tolerance analysis of the design results shows that the RMS value and coupling coefficient meet the requirements of space GW detection. Therefore, the proposed design is a good candidate for the Taiji Program.