The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper. A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation. By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously. Additionally, fuel cost, control saturation, chattering phenomenon and parameters selection were taken into account. Satisfaction of the pro-posed guidance schemes of the saddle point condition is proven theoretically. Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches. Comparison of control performance between different guidance schemes are presented and analysis.