The optical Kerr effect in a quantum disc is investigated with the density-matrix approach, most emphasis isdevoted to the electron-phonon interactions on the optical Kerr effect. The numerical results are presented with characteristic parameters of a GaAs quantum disc. It is shown that the optical Kerr effect increases as the discthickness D decreases. LO-phonons impose greater influence on the optical Kerr effect than SO-phonons. The smaller the disc thickness D, the sharper the peak, and the larger the peak intensity. When the disc thickness is greater than 30, the peak will disappear gradually.