A theory of photon-assisted impact ionization in solids is presented. Our theory makes a quantum description of the new impact ionization-cold avalanche ionization recently reported by P. P. Rajeev, M. Gertsvolf, P. B. Corkum, and D. M. Rayner [Phys. Rev. Lett. 102, 083001 (2009)]. The present theory agrees with the experiments and can be reduced to the traditional impact ionization expression in the absence of a laser.