Aiming at the slow convergence speed of gradient descent(GD) algorithm, a finite impulse response(FIR) dispersion equalizer based on GD optimization algorithm is proposed. The momentum gradient descent(MGD) algorithm is used to optimize the gradient exponentially weighted average(CMGD algorithm for short) and correct the deviation at each update iteration. The single carrier coherent optical transmission system is built by optisystem and simulated with MATLAB. The simulation results show that when the learning rate is 0.1 and the momentum coefficient is 0.98, the convergence value of CMGD algorithm reaches 0.015461. Under different SNR conditions, the equalization effect of the equalizer designed by CMGD algorithm is better than that of GD-FIR and classical time-domain FIR, and the hardware implementation complexity is reduced.