Lefschetz fibrations are one of the important tools in symplectic topology and Homological Mirror Symmetry. Thus, it would be natural to ask how to construct Lefschetz fibrations on symplectic manifolds if they admit Lefschetz fibrations. In this talk, I will introduce an algorithm that produces Lefschetz fibrations on the cotangent bundles. The input of the algorithm is a handle decomposition of the zero section.