In this work we derive an analytic solution for Dirac equation coupled with a strong electromagnetic wave in the presence of ambient plasma. The new solution, which is a generalization of the familiar Volkov solution, enables us to obtain explicit expressions for the wave function, the momentum and the effective mass of the electron as well as the acceleration it experiences in its rest frame (which is the key parameter for QED processes in intense electromagnetic fields). Moreover, the generalized Volkov wavefunction can be applied to various important QED processes, such as nonlinear Compton and nonlinear Breit-Wheeler in the presence of plasma. These processes are fundamental for the understanding of interaction between ultra-high intensity laser and dense matter.