Abstract: The fragmentation initiation threshold velocity for spherical projectiles impacting on thin walls at hypervelocity is mainly determined by experiments and numerical simulations currently. In this study, a theoretical approach for solving fragmentation initiation threshold velocity of projectiles was presented. Theoretical models were established to describe the feature point velocity at the tail of projectiles before/after their fragmentation initiation. Based on the critical condition that the two velocity models were equal, the projectile fragmentation initiation threshold velocity under various bumper-thickness-to-projectile-diameter ratios (t/D) were theoretically solved and compared with the data from Piekutowski experiment and related empirical data. Furthermore, the FE-SPH adaptive coupling method was utilized to theoretically simulate an aluminum projectile impacting on an aluminum bumper at hypervelocity. The working conditions on both sides of the predicted value of the fragmentation initiation threshold velocity were numerically simulated for validation. The analysis indicates that the theoretically predicted results conform well with the experimental and the numerical simulation results. The approach may be extended to diverse materials of spherical projectiles impacting on thin-walled bumpers at hypervelocity. It is of reference for guiding the design of Whipple protective structures.