The optical Kerr effect in cylindrical quantum wires is investigated with density matrix approach,most emphasis is devoted to the electron-phonon interactions on the optical Kerr effect. With characteristic parameters pertaining to GaAs quantum wire,the numerical results are presented. It is shown that,the optical Kerr effect increases as the wire radius R₀ decreases;the optical Kerr considering the electron-LO-phonon interactions is over twenty percent greater than the one without considering the electron-phonon interactions;the smaller the wire radius R₀,the sharper the peak will be,and the larger the peak intensity will be;when the wire radius R₀ is greater than 40 nm,the peak will disappear gradually.