The superconducting transition temperatureT_c for semimetals like bismuth has been calculated as a function of the densityn_c of the electron and hole charge carriers. A simplified two-band model for describing the longitudinal dielectric function for such a system has been used in our model calculation. We find that the attractive interaction responsible for the instability of the normal ground state comes not only from the exchange of lattice phonons, but also from the electronhole sound mode, provided the ratio of the averaged hole to electron mass,m_h/m_e ≠ 1. We have compared our theoretical values ofT_c(n_c) with experimental results for bismuth under hydrostatic pressure, and find reasonable agreement ifm_h/m_e is assumed to have a value which is only slightly larger than that at atmospheric pressures. A linear variation of the negative band gap as a function of pressure has been assumed for the sake of this comparison.