  First-principles calculations are performed for electronic structures of two
high pressure phases of solid selenium, $\beta$-Po and bcc.
  Our calculation reproduces well the pressure-induced phase transition from
$\beta$-Po to bcc observed in selenium.
  The calculated transition pressure is 30 GPa lower than the observed one, but
the calculated pressure dependence of the lattice parameters agrees fairly well
with the observations in a wide range of pressure.
  We estimate the superconducting transition temperature $T_{\rm c}$ of both
the $\beta$-Po and the bcc phases by calculating the phonon dispersion and the
electron-phonon interaction on the basis of density-functional perturbation
theory.
  The calculated $T_{\rm c}$ shows a characteristic pressure dependence, i.e.
it is rather pressure independent in the $\beta$-Po phase, shows a
discontinuous jump at the transition from $\beta$-Po to bcc, and then decreases
rapidly with increasing pressure in the bcc phase.
