The traditional guidance law only guarantees the ac-curacy of attacking a target. However, the look angle and ac-celeration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation (PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish three-dimensional kinematic engagements. The constraints and the per-formance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the opti-mization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.