Abstract: The existence of exponential attractor for the 2D Navier-Stokes equation with damping term is studied. In this paper we discuss the existence of weak solutions and strong solutions for the damping term cu^βu at β≥0 and 1/3≤β≤2 respectively and further proves the existence of bounded absorbing set and satisfying condition C of solution semigroups, thus obtains the exponential attractor of the 2D Navier-Stokes equation with damping term.

Key words: 2D Navier-Stokes equation, damping term, exponential attractor