This talk is concerned with a leader-follower stochastic differential game with asymmetric information, where the information available to the follower is based on some sub-σ-algebra of that available to the leader. Such kind of game problems haswide applications in finance, economics and management engineering such as newsvendor problems, cooperative advertising and pricing problems. Stochastic maximum principles and verification theorems with partial information will be presented. As an application, a linear-quadratic leader-follower stochastic differential game with asymmetric information is studied. It is shown that the open-loop Stackelberg equilibrium admits a state feedback representation if some system of Riccati equations is solvable. This talk is based on a joint work with Shi and Wang.