The high-precision requirements of space gravitational wave detection and the limitation of laser line width and adjustment bandwidth put forward higher requirements for the design of the controller for realizing the optical phase lock of the response intersatellite laser interferometer. However, how to improve the system's suppression of laser phase noise when the control bandwidth is limited is a problem to be solved at present. In this paper, an internal model extended output feedback LQR controller is designed to improve the suppression of the phase noise of the laser under the premise of ensuring the stability of the phase-locked system and no cycle slip phenomenon. The simulation experiment results show that compared with the existing PI controller, under the control bandwidth of 20KHz, the controller designed in this paper can improve the laser phase noise suppression effect by 3 times. This controller reduces the control system's constraint on the maximum line width of the laser.