The rates of scattering by confined longitudinal optical phonons in one-dimensional quantum wires are calculated by taking into account the intra-collisional field effect (ICFE) associated with high electric fields. It is shown that the scattering rate becomes asymmetric with respect to the direction of the electron propagation due to the ICFE. In particular, the energy dependence and strength of the backward scattering are greatly modified by the ICFE. Asymmetry in the scattering rates is noticeable even when multi-subband scatterings are significant in thick quantum wires.