  In this paper, we focus on the moduli space of Seiberg-Witten equation on
non-compact manifold with periodic end. Suppose that the scalar curvature on
the periodic end is identically zero and the topological conditions: the first
de-Rham cohomology and the self-dual cohomology restricting on the periodic end
vanish. Then, we will show that the moduli space of the perturbed
Seiberg-Witten equation is compact.
