According to the trajectory specialty of hypersonic boost-glide vehicles, a strapdown inertial navigation system/BeiDou navigation satellite system (SINS/BDS) algorithm based on the launch-centered inertial (LCI) frame for hypersonic vehicles is proposed. First, the related frame system, especially the launch earth-centered inertial (LECI) frame, and the SINS mechanization in the LCI frame are introduced. Second, SINS discrete updating algorithms in the LCI frame for the compensation of coning, sculling, and scrolling effects are deduced in the attitude, velocity, and position updating algorithms, respectively. Subsequently, the Kalman filter of the SINS/BDS integrated navigation in the LCI frame is obtained. The method of converting BDS receiver position and velocity from the Earth-centered Earth-fixed (ECEF) frame to the LCI frame is deduced through the LECI frame. Finally, taking the typical hypersonic boost-glide vehicles as the object, the SINS/BDS algorithm vehicle field test and hardware-in-the-loop simulation are performed.