Based on Lyapunov stability theory and LaSalle invariance principle, the theorem of linear generalized synchronization for uncertain complex dynamical networks was proposed, where a suitable adaptive controller was designed. It is shown that the linear generalized synchronization between uncertain complex dynamical networks can be realized, and the parameter update laws for identifying the unknown parameters of complex dynamical network are also gained. The controller is feasible and robust for one kind of uncertain complex networks due to its adaptability. The numerical simulations demonstrate the validity and feasibility of the proposed theorem.