In this paper, we have developed a homology theory for finite spaces based on functions from Sierpinski topological space and its product topology to the finite space under consideration, which was called Sierpinski-cubical-singular homology. This homology satisfied all the Eilenberg-Steenrod axioms of homology theory' and thus isomorphic to the well-known homology theories such as simplicial homology theory, singular homology theory, etc. for finite spaces