This paper is concerned with the input-output finite-time mean square stabilization problem for a class of nonlinear semi-Markovian jump systems (SMJSs) with time-varying delay. Both time-varying factors of transition rates and states delay are considered to be bounded. Our main purpose is to derive some parameter-dependent sufficient criteria by designing a state feedback controller, to guarantee the input-output finite-time mean square stabilization for the underlying systems where the nonlinear term satisfies the conic sector constraint. Then, the stabilization conditions are obtained by employing a novel Lyapunov-Krasovskii functional, differential form Gronwall's inequality, and an extra slack variable which is composed of the time-varying transition rates. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed method. (C) 2019 Elsevier Ltd. All rights reserved.