This paper tackles the observer-based finite-time H∞ control problem for networked nonlinear semi-Markovian jump systems (SMJSs) with actuator fault, parameter uncertainties and partly unknown transition rates via an improved dynamic event-triggered scheme (DETS). In comparison with traditional dynamic event-triggered scheme, the observer-based improved dynamic event-triggered scheme which is not restricted by real system states and could save more network resources is firstly proposed in this paper. Then, a more general actuator fault model is considered and the reliable observer-based state feedback controller is designed. Sufficient conditions are proposed to guarantee the closed-loop system is stochastically finite-time bounded with a prescribed H∞ disturbance attenuation level. Lastly, two simulation examples are given to affirm the validity of the results obtained in this paper.