A guidance approach is presented for the intercept of near space hypersonic gliding targets. Two typical maneuvers of the gliding entry trajectory are analyzed. The trajectory for a boost-glide interceptor is designed, and the whole trajectory is divided into four phases including the boost phase, the glide phase, the aiming phase and the hit-to-kill phase. In the glide phase, a guidance method based on the velocity error corridor and the modified quasi-equilibrium glide condition is proposed. In the aiming phase, a guidance approach is designed based on the lift control. In the hit-to-kill phase, a guidance algorithm using the reaction-jet control is employed. Finally, the intercept trajectory is simulated in two typical missions. Results show that the miss distance is within 0.2 m, thus a hit-to-kill performance is achieved by the interceptor. The intercept strategy and the guidance methods in different phases are demonstrated to be effective.