An involute guidance laws with terminal velocity direction constraint have been proposed for terminal maneuver unpowered reentry vehicle. According to the flight characteristics of unpowered vehicles and the geometric properties of the involute of a circle, an involute trajectory was generated by two positions of vehicle and target and an impact angle between the desired terminal velocity and line of sight. And a 3-D trajectory tracking guidance method is designed based on the error of flight path angle and heading angle for achieving accurate tracking of the involute trajectory. Simulation results demonstrated that the involute guidance laws can guide the vehicle accurately arriving the target point with the directed the terminal impact angle constraint, and are superior to the circular guidance laws in curvature, required acceleration and terminal speed. The involute guidance laws have a high engineering application value.