Free-form surface reflector has the ability to correct the wave-front distortion of high power soild-state laser systems.Using free-form surface reflector for wave-front correction has high requirement for the accuracy of processing and design.Based on the complementary principle of wave-front,a free-form surface reflector was designed.The surface was reconstructed by BP neural network algorithm,and the free-form surface equation with high accuracy was fitted which meets the requirement of numerical control machining.