This article is concerned with the tracking control problem for uncertain high-order nonlinear systems in the presence of input saturation. A finite-time control strategy combined with neural state observer and command filtered backstepping is proposed. The neural network models the unknown nonlinear dynamics, the finite-time command filter (FTCF) guarantees the approximation of its output to the derivative of virtual control signal in finite time at the backstepping procedure, and the fraction power-based error compensation system compensates for the filtering errors between FTCF and virtual signal. In addition, the input saturation problem is dealt with by introducing the auxiliary system. Overall, it is shown that the designed controller drives the output tracking error to the desired neighborhood of the origin at a finite time and all the signals in the closed-loop system are bounded at a finite time. Two simulation examples are given to demonstrate the control effectiveness.