We have performed first-principles calculations of the structural stability, superconductivity, and anharmonicity of phosphorus under high pressure. The simple hexagonal (sh) structure transforms into an experimentally observed cI16 structure via a body-centered cubic (bcc) structure. In the transition from an sh into bcc structure, the superconducting critical temperature T_c increases from 0.5 to 12 K, which is the highest T_c in phosphorus. It decreases to 6 K in the transition into the cI16 phase. The pressure-dependence of T_c is related to that of the density of states at the Fermi level. In addition, we investigated anharmonicities in phosphorus under high pressure.