The one- and the two-photon absorption rates of conduction-band electrons (CBEs) in dielectric materials are calculated by second-and third-order perturbation theory, respectively. Here fused silica irradiated under 526 nm ultra-short pulse laser is used as an example. Compared with the case that only the one-photon absorption of CBE assisted by a phonon is considered. the rate of total energy gain of CBE from laser field will be enhanced by a factor of 3 when both of the one-and the two-photon absorption are included. The avalanche rate includes not only the term proportional to laser intensity, but also the terms proportional to the square of laser intensity and to the product of laser intensity and hole density. The damage threshold is calculated on the basis of the avalanche model, and find it is lowered by about 15% compared with the case for only the one-photon absorption of CBE assisted by a phonon is considered. The theoretical value agrees well with experimental results.