This technical note is concerned with the design problem of adaptive sliding-mode stabilization for Markov jump nonlinear systems with actuator faults. The specific information including bounds of actuator faults, bounds of the nonlinear term and the external disturbance is not available for the controller design. The main attention focuses on designing the adaptive sliding-mode controller to overcome these problems. Firstly, a sliding-mode surface is constructed such that the reduced-order equivalent sliding motion is stochastically stable. Secondly, the adaptive sliding-mode controller can drive the state trajectories of the system onto the sliding-mode surface in finite time, and can estimate the loss of effectiveness of actuator faults and bounds of the nonlinear term and the external disturbance online. Thirdly, the stochastic stability of the closed-loop system can be guaranteed. Finally, a practical example is provided to demonstrate the effectiveness of the presented results.