Abstract: One interesting application of Hirzebruch signature theorem is the construction of exotic differential structure on $S^7$. In this talk I will first show the construction of the exotic $S^7$, which is the sphere bundle of the 4 dimensional vector bundle over $S^4$ by using of the first Pontrjagin class and Euler class. Then for proving it has an exotic differential structure, we use Hirzebruch signature theorem to construct a invariant and compute this invariant for standard $S^7$ and our sphere bundle to see they are different.