This paper investigates the finite-time stabilization of a class of switched stochastic nonlinear systems in p-normal form, where the power orders of the system are dependent upon the switching signal and the system structure is in non-triangular form. Compared with the existing results, some power orders of the system are allowed to be even. Under suitable assumptions, a state feedback control law with state-dependent switching is designed by using the convex combination method and the adding a power integrator technique. It is shown that the resulting closed-loop system is finite-time stable in probability. Simulation results of a continuously stirred tank reactor (CSTR) system are provided to show the effectiveness and applicability of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.