Linear quadratic regulator (LQR) is an optimal controller being used for linear systems, and it can minimize the comprehensive quadratic performance index (QPI) with respect to convergence error and control consumption. However, LQR lacks the robust property to cope with parameter perturbations and external disturbances. Aiming at the above deficiency of LQR, a robust LQR (RLQR) is proposed for linear systems under the guideline of planes cluster approaching mode (PCAM). In the proposed RLQR, one nonlinear item is introduced into control law, and it cooperates with the other linear item to guarantee the global asymptotic stability in the presence of equivalent disturbances. The conditions of global asymptotic stability are deduced by the method of Lyapunov function. Simulation results present that, the chosen LTI plant using RLQR possesses smaller QPI in the existence of time-varying disturbances, compared with the conventional LQR and sliding mode controller (SMC).