For the ball and plate system where the strong coupling and the uncertainty of friction force are existed, an indirect adaptive control method is proposed by using the Lyapunov stability theory. The proposed system not only can ensure all variables in the system are bounded, and keep the convergence property of the tracking error of the ball and plate system, but also can ensure the stability and the tracking error of that are converged to a small neighborhood of the origin. The proposed indirect fuzzy controler consists of a supervisory control term, an indirect fuzzy control term, and an adaptive compensation control term. The simulation results show that the proposed approach guarantees the stability and control performance of the nonlinear multivariable ball and plate system trajectory tracking control.