We give a construction of a state sum invariant of closed spin 3-manifold based on super 3-cocycle (a, ω) and combinatorial representation of spin 3-manifold, where ω is a Z2-valued cocycle and a is a 3-cochain satisfying a 3-cocycle condition with a sign coming from the 2-cocycle ω. The definition of the invariant is similar to the state sum construction of the Dijkgraaf-Witten invariant, except it uses the spin structure to take care of the sign in the 3-cocycle condition. We also give an example of the invariant and see that it is sensitive to the spin structure