Adopting basic-differential equations for self-simulating motion of one-dimensional nonstable flow in ideal gas, the self-simulating characteristics of wave-rear gas in spherical strong shock wave have been analyzed in detail. Additionally, the general form of propagation formula for the spherical strong shock wave,owning self-simulating motion characteristics, is deduced out. Study indicates that the self-simulating motion mode of spherical strong shock wave need not start from a point having irregularity, and the initial shock velocity and self-simulating temperature function, generally, do not exist the problem of driving to infinite. And, Taylor’s self-simulating mode of the shock wave from point explosion is a special case of the general self-simulating mode with the assumption that the whole energy of the self-simulating motion is a definite value.