Analytic torsion is a secondary topological invariant that could distinguish between closed manifolds which are homotopy equivalent but not homeomorphic. It can be defined analytically in terms of the determinant of Hodge Laplacian. In this talk, I will explain how Witten Laplacian can be used to generalize this construction to vector bundles over closed manifolds. I will also discuss how to relate the index and the analytic torsion of the total space to those of the base manifold. This is a joint work with Xianzhe Dai.