A finite-time adaptive neural network dynamic surface tracking control scheme is proposed for a class of uncertain multiple-input multiple-output strict-feedback nonlinear systems with nonconvex input constraint and external disturbance. Firstly, by introducing a nonconvex constraint operator, the designed feedback control input is transformed into the actual input vector with the largest value in the same direction, thus the actual control input is always kept in the nonconvex constraint set. Secondly, the radial basis neural network is used to approximate the uncertain continuous function vector to solve the control problem with unknown upper and lower bounds of the control gain matrix, and the inequality reduction is utilized to deal with the unknown bounded disturbance. Then, a finite-time adaptive dynamic surface tracking controller using the backstepping approach is proposed to ensure that all signals of the closed-loop system are ultimately uniformly bounded, and to realize the finite-time tracking control of the desired trajectory. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control scheme.