A robust adaptive control scheme is designed for a class of pure-feedback nonlinear systems with non-affine functions possibly being discontinuous.The continuous and bounded conditions on non-affine functions are relaxedand the bounds of non-affine function are unknown continuous functions.Moreoverthe problem of computational complexity caused by the repeated differentiations of virtual control laws is eliminated by utilizing dynamic surface control technique.It is proved theoretically that all the signals in the closed-loop control system are semi-globally uniformly ultimately boundedand the system output can asymptotically converge to an arbitrarily small neighborhood of the equilibrium point by choosing the appropriate design parameters.Finally simulation examples are provided to demonstrate the effectiveness of the designed approach.