While testing the secondary mirror with convex aspheric of off- axis three- mirror optical system, compensation method is used to achieve high-precision aspheric testing. Thus design of compensator is a key technology. Compensation in transmission form can′t be used for small- caliber convex aspheric surface with great quadratic surface coefficient and non- transmissive back surface. So the convex aspheric surface is directly taken as a reflection in auto- collimation parallel light compensation test. According to the design ideas, the initial structure is built by the Zemax firstly, which simplifies the calculation of the initial structure, and can get the desired compensation system structure. The design and tolerance analysis process of convex aspheric secondary mirror compensator system is given with the diameter of 80 mm, the quadratic surface coefficient of - 6.5, and the F number of 5.00375. The system operating wavelength is 632.8 nm. The root mean square (RMS) of wavefront error is 0.000015λ. Analysis results show that the total residual wave aberration of the system is 0.0104708λ, which satisfies the requirement of assembling accuracy.