This paper addresses the \(H_\infty \) control problem for time-varying networked control systems (NCSs) under the FlexRay protocol (FRP), considering packet loss and general sensor and actuator faults. In particular, the general faults are considered for the first time in such a problem, where each mode of component fault includes multiplicative and additive time-varying fault types. Firstly, in order to deal with network congestion due to the limited bandwidth, the FRP is used to schedule the information exchange. This paper presents the first simultaneous consideration of the FRP and packet loss in the communication network in NCSs. Subsequently, models are separately established to characterize the phenomena of packet loss and general sensor and actuator faults in time-varying NCSs. Based on this, a FRP-based comprehensive system model is then provided and a mode-dependent fault-tolerant controller is designed. In addition, sufficient conditions for the mean square asymptotic stability (MSAS) of the closed-loop system are proposed by using the Lyapunov stability theory and average dwell time (ADT) constraints. In order to solve the controller gains, the cone complementarity linearization (CCL) algorithm is employed to solve the non-convex problem. Finally, two numerical simulations with a theoretical example and a practical example demonstrate the effectiveness and feasibility of the proposed method.