The effects of confinement and magnetic fields on the effective electron Landé g factor of GaAs–Ga1−xAlxAs cylindrical quantum well wires are studied. Calculations were carried out via the Ogg–McCombe effective Hamiltonian which is used to describe the non-parabolicity and anisotropy effects on the electron states in the conduction band. The applied magnetic field is taken along the wire axis, and the Schrödinger equation corresponding to electron spin projections parallel and antiparallel to the magnetic field is solved by using an expansion of the electron wavefunctions in terms of two-dimensional harmonic oscillator wavefunctions. Calculations for the electron factor in GaAs–Ga1−xAlxAs cylindrical quantum well wires are compared with results from previous theoretical work. Moreover, the present results clearly indicate the importance of taking into account the non-parabolicity/anisotropy of the conduction band if one is interested in a quantitative understanding of the electron g factor in GaAs–Ga1−xAlxAs quantum well wires.