The adaptive coupling of the laser beam from space to single-mode fiber plays an important role in free space optical communication. A typical adaptive algorithm is stochastic parallel gradient descent algorithm (SPGD), which measures the performance index value to estimate the gradient value to maximize the coupling efficiency. It is conceivable that the presence of performance index measurement noise will have a great influence on the convergence performance of the algorithm. We propose an improved Kalman stochastic parallel gradient descent algorithm (KSPGD). Specifically, considering the influence of measurement noise on gradient estimation, we introduce the gradient prediction model in the iterative optimization process and then use the Kalman filter to estimate the gradient of the current iteration point. Kalman filter algorithm and optimization algorithm are integrated together. Simulation and experimental results show that the KSPGD algorithm can better restrain the influence of measurement noise on the convergence performance of the algorithm than the SPGD algorithm.