A reentry trajectory for a hypersonic vehicle with an accessory rocket-powered engine is optimized in terms of the ignition time of boosters and the fuel consumption, based on which a reentry mode of range-extended trajectory is proposed. The analytical solution of Sanger trajectory reveals the conditions of the attack angle and initial velocity for the vehicle to travel the longest distance, which can be used to manipulate the boosters with the goal of maximum travel distance and minimum fuel consumption. The reentry trajectory is designed as a combination of Sanger trajectory and quasi-equilibrium glide trajectory. In the first stage of reentry, the vehicle flies along an equal altitude quasiperiodic trajectory guaranteed by boosters interval ignition, and ensures that the range is longest. In the second stage of reentry, the vehicle flies along a quasi-equilibrium gliding trajectory which is the solution of an optimal control problem with trajectory smoothness and distance as the performance index and the problem is converted and solved by constrained nonlinear programming. Finally, the proposed reentry trajectory is simulated and the results show that the trajectory is quite analogous to the so called "stone skipping" under the conditions of sufficient fuel and appropriate path angle, which can efficiently use its mechanical energy of a stone to long range over a lake. Compared with the trajectories with boosters working in different modes and the trajectories solved in different ways, the proposed reentry trajectory has 3.47-3.84 times range, 1.04-1.18 times end kinetic energy and 4.47-15.79 times fuel availability.