Synchronization problem for a class of complex networks consisting of N nonlinear dynamical nodes that are nonlinearly and diffusively coupled is solved in here. The global synchronization of such networks is investigated via Lyapunov stability theory. Under assumptions that measurements full state vectors of each node are available and coupling coefficients are known, a family of decentralized nonlinear feedback controllers are designed to globally synchronize the network system. When coupling coefficients are unavailable, an adaptive mechanism is introduced to synthesize a family of decentralized adaptive controllers which guarantee the global synchronization. An illustrative example with Lorenz node systems along with the respective computer simulation results is given to demonstrate the effectiveness of the proposed solution to controlled synchronization.