This paper addresses a finite-time sliding-mode control problem for a class of Markovian jump cyber-physical systems. It is assumed that the control input signals transmitted via a communication network are vulnerable to cyber-attacks, in which the adversaries may inject false data in a probabilistic way into the control signals. Meanwhile, there may exist randomly occurring uncertainties and peak-bounded external disturbances. A suitable sliding mode controller is designed such that state trajectories are driven onto the specified sliding surface during a given finite-time (possibly short) interval. By introducing a partitioning strategy, the stochastic finite-time boundedness over the reaching phase and the sliding motion phase is analyzed, respectively. A key feature is that a set of mode-dependent sufficiently small scalars are introduced into some coupled Lyapunov inequalities such that the feasible solutions are easily obtained for the stochastic finite-time boundedness of the closed-loop systems. Finally, the practical system about a single-link robot-arm model is given to illustrate the present method.