Abstract We calculate the electron-phonon contribution to the ground-state energy of a quasi- one-dimensional gas of interacting polarons by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The Hartree-Fock and RPA results are also presented for comparison. We have found that screening effects on the electron-electron and electron-phonon interactions are more effective in quantum wires of small sizes. We also notice that correlation and exchange effects are more evident in wires of reduced dimensions.