This article addresses the problem of finite-time neural network (NN) adaptive dynamic surface control (DSC) design for a class of single-input single-output (SISO) nonlinear systems. Such designs adopt NNs to approximate unknown continuous system functions. To avoid the “explosion of complexity” problem, a novel nonlinear filter is developed in control design. Under the framework of adaptive backstepping control, an NN adaptive finite-time DSC design algorithm is proposed by adopting a smooth projection operator and finite-time Lyapunov stable theory. The developed control algorithm means that the tracking error converges to a small neighborhood of origin within finite time, which further verifies that all the signals of the controlled system possess globally finite-time stability (GFTS). Finally, both numerical and practical simulation examples and comparing results are provided to elucidate the superiority and effectiveness of the proposed control algorithm.