Taking ballistic missile interceptor in the atmosphere as the research object,the terminal guidance problem of the interceptor is studied.The definition of predicted hit point is given,the generalized predicted hit point is derived,and approximate theory is used to get its mathematical expression.Then,based on classical differential geometry,the curvature and torsion instructions of the differential geometry guidance law are derived.The differential geometry guidance law is designed based on the predicted hit point for use in the ballistic missile interception scene.On the basis of this guidance law,by introducing the autopilot and seeker equivalent models,the influence of the guidance control system on guidance accuracy is analyzed.By comparison with the two other guidance laws through simulation,it is demonstrated that the differential geometric guidance law based on predicted hit points has the superiority of reducing the required overload and the line-of-sight angular velocity.