In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller.