The properties of the conduction-electron g ∥ factor in semiconductor GaAs– Ga 1 - x Al x As quantum-well wires under magnetic fields applied along the wire axis are presented. The electron g ∥ factor is obtained as a function of both the applied magnetic field and transversal area of the wire. Calculations are performed by taking into account the non-parabolicity and anisotropy of the conduction band via the Ogg–McCombe Hamiltonian for both cylindrical and rectangular quantum-well wires. The conduction-electron Landé factor is shown to be a growing function of the applied magnetic field as well as dependent on the shape of the transversal section of the wire.