Most existing methods for finite-time stabilizing controller design of linear time-varying systems involve solving differential linear matrix equations. Due to the non-convexity of the problem, it requires a high computational burden. This paper proposes a numerical method to solve finite-time stabilization problems. Successive approximations are performed to estimate the evolution of system states. Accordingly, a gain-switched state feedback controller can be obtained by solving a sequence of linear matrix inequalities (LMIs) based optimization problems. The proposed algorithm is used to design the mass-spring system and the autopilot system of the BIT missile. Comparison with existing methods is given and the simulation results show the effectiveness of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.