In order to reduce the noise content of the fiber optic gyro (FOG) output signal, and to improve the zero drift index of the FOG, the paper uses the programmable logic device FPGA. The LMS algorithm is analyzed and studied, and it is realized by Verilog language programming. The thought of the paper is based on classical finite state machine. Compared with previous programming algorithms, it has a great progress on both structures and the resource utilization. The design of the adaptive filtering algorithm on the off-line state verifies the rationality of the simulation of the signals by using Modelsim, and output the filtering results, that are analyzed in MATLAB. The adaptive filter designed can reduce the white noise in the output data of the gyros, and improves the zero drift performance of the FOG effectively.