In this paper, Η$_{infty}$ depth and course controller of an AUV(Autonomous Underwater Vehicle) using Η$_{infty}$ servo control is proposed. The Η$_{infty}$ servo problem is formulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the Η$_{infty}$ servo problem is as fellows: first, this problem is modified as an Η$_{infty}$ control problem for the generalized plant that includes a reference input mode, and then a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach. The Η$_{infty}$ depth and course controller are designed to satisfy with the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under disturbances(wave force, wave moment, tide). The performances of the designed controllers are evaluated with computer simulations, and finally these simulation results show the usefulness and application of the proposed Η$_{infty}$ depth and course control system.