In the process of the quantum key distribution based on the polarization coding of photons, the polarization state will be affected strongly and randomly by the birefringence effect of the single-mode fibers, which will lead to decrease the final secure key rate. Fortunately, this undesirable effect of single-mode fibers can be corrected by the combination of two quarter-wave plates and a half-wave plate. Utilizing the combination of three wave plates as the actuator, we build a simulation model of real-time polarization compensation based on stochastic parallel gradient descent algorithm. We study the relationship among the amplitude of the random disturbance, the gain factor and the convergent rate. Furthermore, we implement an experiment to demonstrate the algorithm we proposed. The results of the experiment show that the polarization extinction ratio of the simulation system can be corrected well after a certain number of iterations.