In this paper, the time-domain finite element method (TDFEM) is employed to analyze the high power breakdown in air. During the breakdown process, the motion of free electrons generates plasma currents, which produce secondary fields that couple back into the externally applied fields and interact with the free electrons. Such a breakdown process can be described by a coupled electromagnetic-plasma system, where the electromagnetic fields are governed by Maxwell's equations and the plasma current is modeled by a simplified plasma fluid equation. Due to the nonlinear characteristics of the breakdown phenomenon, the coupled system results in a nonlinear second-order partial differential equation that is solved by TDFEM together with the Newton-Raphson method. A numerical example is given to demonstrate the nonlinear characteristics of the breakdown phenomenon and the self-sustaining property of the plasma current.