Seiberg-Witten monopole equations are defined on 4-manifolds and solution space of this equations yields differential topological invariants. In this work we consider 8-dimensional Riemannian manifolds with structure group Spin(7). Such manifolds have a distinguished 4-form. By using this 4-form we define self-dual 2-form in dimension eight which is consistent with the well known self-duality notion in 8-dimension given by CDFN (see [5]). We then express Seiberg-Witten like equations in 8-dimension as analogues of Seiberg-witten equations in 4-dimension.