In order to compensate for the coupling efficiency loss of space optical-single mode fiber caused by random vibration of satellite platform, the influence of parameter selection based on nutation algorithm and random parallel gradient descent (SPGD) algorithm on the stability and convergence speed of the two algorithms is compared and analyzed. The compensation effects of the two algorithms are evaluated under typical satellite vibration spectrum conditions. The simulation results show that the average coupling efficiency of nutation algorithm is 81.26%, and the root mean square error is 7.2×10-4; the average coupling efficiency of SPGD algorithm is 80.72%, and the root mean square error is 1.9×10-3. Compared with SPGD algorithm, the root mean square error of nutation algorithm is reduced by 62.1% in the optimal case, and its stability is better.