An on-line suboptimal midcourse guidance law, which is a neural-network approximation of the optimal feedback strategy, is proposed to eliminate the need for solving two-point boundary-value problems in real time. For intercept point prediction, a fast conversing, iterative algorithm based on a neural- network time-to-go estimator is devised. Also. the γ-correction guidance law and the $\dot{σ}$-feedback guidance law are devised to improve the neural-network guidance to be robust against missile launch conditions. Then the neural-network guidance is extended for interception of ballistic targets in the three-dimensional space. The fact that the optimal trajectory in the three-dimensional space does not deviate much from a vertical plane justifies the use of the two-dimensional neural-network method. Computer simulation confirms that the closed-loop behavior of the proposed guidance law is so close to the optimal trajectory that it outperforms nonoptimal guidance laws such as -biased proportional navigation.