Since the first detection of gravitational wave, gravitational wave astronomy has advanced swiftly. As a crucial component of the detection system, the gravitational wave telescope is obviously crucial. The highly stable laser telescope with a low wavefront error and a high suppression ratio of stray light is a crucial medium for the detection of gravitational waves, as it must not only transmit energy in the order of watt to distant spacecraft, but also receive weak laser signals in the order of picowatt from other satellite base station located millions of kilometers away. Therefore, the backward stray light of the local telescope is required to reach 10^-10 orders of the incident laser power. Considering the requirements of small size, light weight, and high compactness, it is clear that the benefits of a reflective system cannot be compared to those of a transmission design. In general, the coaxial Cassegrain structure and off-axis multi-mirror structure are utilized. The off-axis design is preferred over the coaxial design for gravitational wave telescopes due to advantages such as the ability to optimize multiple parameters, the absence of a central obstruction, and the high energy collection capacity. In this paper, based on the design of off-axis four-mirror and the theory of coaxial reflection system, we designed and optimized the telescope combined with the characteristics of high magnification, low wavefront error and high suppression ratio of stray light. In the capture field of view of ±200 μrad, we realized the compression ratio of 100 of telescope, and the entrance pupil diameter of the principle system is 300 mm, whose design result of wavefront error is less than of λ/80 because the actual outgoing wavefront error must be less than λ/40. The system distortion of the edge field is less than 0.056 9%. In order to verify the processing and alignment of the principle system as well as the ability of stray light suppression of it, a 0.5 times scale system is established beneath the system with a wavefront error less than λ/175. Internal stray light is suppressed by increasing the light turning angle between the tertiary mirror and quaternary mirror on the condition of low wavefront error of λ/80. The optimized deflection angle of the tertiary mirror is 5.5 degrees, and the tertiary mirror is the plane surface, which can significantly reduce the difficulty of processing and alignment. A simulation of stray light is applied to analyze the stray light of our designed telescope. The steps of stray light analysis consist of the following steps: 1) selection and optimization of the optical structure; 2) model setting of the corresponding reflection, scattering, and absorption surfaces; 3) stray light analysis of the entire system; 4) iterative optimization design; 5) fulfillment of the system's requirements. Therefore, we investigated the optical paths and power of the backscattered stray light. After positioning the field stop in the middle image plane between the secondary mirror and the tertiary mirror, the proportion of the stray light caused by the secondary mirror is the smallest. The stray light energy caused by the tertiary mirror and the quaternary mirror is the largest, which can reach more than 90%. The tolerance of the optical design is also analyzed, and the results of the analysis indicate that the tolerance of the parabolic primary mirror has the strongest impact on the wavefront error of the system. The principle system has a 90% cumulative probability wavefront error less than λ/40, which can satisfy the design requirement of gravitational wave detection and have the potential to play a significant role in future missions aimed at low wavefront error, high magnification and a high suppression ratio of stray light in the telescope while detecting gravitational waves.