We present results of ab initio theoretical investigations of the electronic structure, phonon dispersion relations, electron-phonon interaction and superconductivity in the rocksalt and tungsten-carbide phases of CrC. It is found that, compared to the stable tungsten-carbide phase, the metastable rocksalt phase is characterized by a much larger electronic density of states at the Fermi level. The phonon spectra of the rocksalt phase exhibit anomalies in the dispersion curves of both the transverse and longitudinal acoustic branches along the main symmetry directions. A combination of these characteristic electronic and phonon properties leads to an order of magnitude larger value of the electron-phonon coupling constant (λ = 2.66) for the rocksalt phase compared to that for the tungsten-carbide phase (λ = 0.24). Our calculations suggest that superconducting transition temperature values of 0.01 K and 25-35 K may be expected for the tungsten-carbide and rocksalt phases, respectively.