We propose and investigate a new general model of fuzzy complex network systems described by Takagi-Sugeno (T-S) fuzzy model with time-varying delays. Hybrid synchronization problem is discussed for this general T-S fuzzy complex dynamical network with nondelayed and delayed coupling between nodes. Utilizing Lyapunov-Krasovskii functional method, synchronization stability criteria for the networks are established in terms of linear matrix inequalities (LMIs). These criteria reveal the relationship between coupling matrices with time-varying delays and synchronization stability of the dynamical network. Numerical simulation is provided to illustrate the effectiveness and advantage of derived theoretical results.