Aiming at correcting static aberrations of telescope for quantum communication and improving the energy concentration of receiving signal light, the method of static aberration correction based on stochastic parallel gradient descent (SPGD) algorithm is proposed. Unlike the conventional adaptive optics systems, the SPGD algorithm does not require the wavefront sensor, and can effectively reduce the complexity of system. An adaptive optics aberration correction test-bed is set up with a 64-element deformable mirror (DM) and a CCD detector. The static wavefront aberrations of a 700 mm telescope is compensated, and the far-field diameter is improved to 30 μm from the original value of 58 μm. The feasibility of SPGD algorithm used to correct static wavefront aberrations of telescope is demonstrated.