Abstract: A new test for steep convex hyperboloidal secondary mirrors with large aperture and fast focus ratio is presented. It makes use of small correcting lens and an auxiliary ellipsoidal mirror which aperture is about 1.8 times as large as that of the convex mirror tested. This method is sutable for convex secondary asphere of very large aperture optical telescope. Taking TMT as an example whose surface is a convex shape with the diameter of 3.1m, fast focus ratio of F/1 and conic constant of -1.318 228, a null compensation system is successfully designed and optimized. The design results indicate that the surface quality of the steep convex hyperboloidal secondary mirror could be measured directly, in addition the aberration of the testing system is well corrected，PV is about /100 and the spot diameter is smaller than the diffraction limit. Analyses of the system-s wave-front error with respect to the change in the surface parameter of optical elements are described.