In this paper, An LQR controller is proposed for way-point tracking of AUV (Autonomous Underwater Vehicle). The LQR controller aims at tracking a series of way-points which operator registers arbitrarily in advance. It consists of a depth controller and a steering controller and AUV's surge speed is assumed varying to consider the dynamic environment of the underwater. In order to show the performance, a conventional state feedback controller is compared with the proposed controller by the simulation using Matlab/Simulink. The parameters of AUV developed by the author's laboratory are used. In the simulation, we verify that the LQR controller can track all the way-points within 1 m error range under the varying surge speed, which proves the robustness of the LQR controller.