Within the effective-mass approximation a simple method to calculate the spectra of a shallowdonor impurity in GaAs±(Ga, Al)As cylindrical quantum-well wires (QWWs) suitable for any confinement potential shape in radial direction is proposed. A trial function is taken as the product of a hydrogenic part with two envelope functions: the ground state wave function of the uncoupled electron in quantum-well wire f k (r), and a variational function j(z) that describes the orbit confinement in axial direction. A Schro È dinger-type equation for j(z) corresponding to the best trial function is deduced. The method is applied to analyze the D 0 ground and first excited states in coaxial cylindrical QWWs. Two peaks in the curve of the 1s-like state binding energy vs. the QWW radius are found.