According to the control requirements of both accuracy and efficiency in random vibration test, a novel control algorithm for power spectral density (PSD) replication based on adaptive inverse control scheme is proposed. The strategy of frequency separation and variable step size is introduced in the Least Mean Square (LMS) algorithm, thus a LMS algorithm suitable for the iteration of PSD is obtained. Through the design of initializing the weight vector with the system pre-identification results, control efficiency is enhanced and the amount of iterative computation can be reduced. In addition, a numerical simulation method based on AR model is applied in order to generate the time-domain drive signal and reproduce the expected PSD accurately by filtering Gaussian white noise signal. The simulation experiment of PSD replication is performed and the result proves the effectiveness of the algorithm.