We explored the feasibility of generating a coherent longitudinal optical (LO) phonon–plasmon coupled mode in an n-type InSb single crystal with the condition that the photo-Dember effect is strongly suppressed and/or eliminated. We systematically performed terahertz time-domain spectroscopic measurements of the n-type InSb single crystal and undoped InSb crystal. The terahertz electromagnetic wave originating from the photo-Dember effect was extinguished in the n-type InSb single crystal, while the clear signal from the photo-Dember effect was detected in the undoped InSb single crystal. Meanwhile we detected the clear signal of the terahertz wave from the coherent LO-phonon–plasmon coupled mode in the n-type InSb single crystal, indicating that the photo-Dember effect is not dominant in the generation of the coherent LO-phonon–plasmon coupled mode although the photo-Dember effect has been attributed to the dominant generation mechanism of the coherent LO-phonon–plasmon coupled mode so far. We explain the present phenomenon, taking account of the fact that the impulsive stimulated Raman scattering process has a possibility of generating coherent LO-phonon–plasmon coupled modes in light-absorbing solids [Nakamura et al., Phys. Rev. B 99, 180301(R) (2019)].