The linear quadratic Gaussian (LQG) control problem for non-stationary stochastic seismic response of adjacent buildings was studied. The motion equations of adjacent buildings connected by hydraulic actuators against earthquake were established. The complex modal superposition method was then used to determine the dynamic characteristics, including modal frequencies and modal damping ratios. The shaping filter was introduced to deal with the power spectral density function of earthquake excitations,and then a closed form solution was derived by combining the pseudo-excitation method and the residue theorem. The results from a numerical example show that,if the parameters of LQG controllers are selected appropriately, the seismic responses of both buildings can be considerably reduced when LQG controllers are used. Moreover，the steady states of seismic response of controlled buildings can be achieved much quickly than the uncontrolled buildings.