A suboptimal midcourse guidance law is obtained for interception of free-fall targets in the three-dimensional (3D) space. Neural networks are used to approximate the optimal feedback strategy suitable for real-time implementation. The fact that the optimal trajectory in the 3D space does not deviate much from a vertical plane justifies the use of the two-dimensional (2D) neural network method previously studied. To regulate the lateral errors in the missile motion produced by the prediction error of the intercept point, the method of feedback linearization is employed. Computer simulations confirm the superiority of the proposed scheme over linear quadratic regulator (LQR) guidance and proportional navigation (PN) guidance as well as its approximating capability of the optimal trajectory in the 3D space.