A multi-input multi-output (MIMO) random vibration control method is proposed for a multi-axis hydraulic shaking table system to replicate the reference power spectral density (PSD). Kinematics analysis is presented to reduce cross-coupling between the axes of the hydraulic shaking table. The time histories generated by time domain randomization in conventional MIMO random vibration control have spectral leakage between the frequency resolutions. The drive signal PSD is used in the proposed control method to design a linear time-invariant system. Circular convolution is then proposed to implement the designed system and convert the PSD to time histories with white noise. Experimental results obtained in step response and two-axis PSD replication show the effectiveness of the proposed control method.