<p>Tail-controlled missiles exhibit non-minimum phase (NMP) characteristics due to a right-half-plane (RHP) zero in their acceleration dynamics, which can lead to internal instability and command divergence during the terminal homing phase. The rapid homing guidance law proposed in Kim and Park (IEEE Trans Aerosp Electron Syst 58:729–742, 2022) effectively addressed high-altitude, short-time engagements by generating jerk-based commands and achieving terminal zero acceleration and zero miss distance, even when applied to arbitrary autopilot dynamics. However, since it relies on feedback linearization for acceleration command generation, it cannot ensure stability when applied to NMP systems. To overcome this limitation, this paper proposes a modified rapid homing guidance law using only acceleration output redefinition, without redesigning the original autopilot. The proposed guidance law enables realizable and internally stable command generation for the NMP system while maintaining terminal performance objectives that minimize the final acceleration and miss distance. Numerical simulations under various conditions demonstrate that the proposed guidance law ensures stability in the presence of the RHP zero and verify its homing performance.</p>