The robust stabilization for a class of nonlinear uncertain neutral systems with multiple time delay is mainly discussed. Because the uncertainty of this class of system is bounded by a linear function of the norm of the delayed states with unknown bounds, an adaptive update law is proposed to estimate the square of these unknown bounds. An adaptive control law is thereafter constructed. It is proved by Lyapunov stability theory that the solution of the closed loop system which includes the original system, the adaptive control law and the update law is uniformly ultimately bounded. Finally, a numerical example is given to demonstrate the effectiveness of the method.