This paper investigates the finite-time control of networked control systems subject to actuator saturation under hybrid attacks. A unified Markov process framework is adopted to model the hybrid attacks, which effectively captures their dynamic nature and facilitates the generalization of attack scenarios. Specifically, a neural network is employed to approximate false data injection attacks within this hybrid framework. Considering limited network resources, a dynamic event-triggered mechanism is introduced to enhance communication efficiency. To account for the effects of network-induced delays and hybrid attacks, a mode-dependent Lyapunov–Krasovskii functional is constructed. Sufficient conditions for finite-time stability are derived, significantly reducing conservatism in the controller design. Based on the stability analysis, the explicit form of the controller is obtained using linear matrix inequality techniques. The effectiveness and superiority of the proposed method are demonstrated through a numerical simulation example.