This paper investigates the adaptive finite-time stabilization of a class of switched nonlinear systems with unknown nonlinear terms using neural networks. Under the assumption that all the growth conditions for the unknown nonlinear perturbation functions are partially known, the common finite-time controller and adaptive law are constructed by extending the adding-a-power-integrator technique and using the backstepping methodology. The unknown parts of the growth conditions are modeled by the neural networks and the known parts are exploited for the controller design. The bounds of neural network approximation errors are assumed to be unknown and are estimated online. It is shown that the state of the closed-loop system is finite-time stable and the parameter estimations are bounded under arbitrary switching. A simulation example is provided to show the effectiveness of the proposed method.