The properties of a hydrogenic impurity in a parabolic GaAs quantum-well wire in the presence of the magnetic field are investigated using the finite-difference method within the quasi-one-dimensional effective potential model. The magnetic effects on the energies and binding energies of the ground and lowest excited states of a hydrogenic impurity in a parabolic GaAs quantum-well wire are studied for various parabolic potentials. The calculated results indicate that the interplay of the spatial confinement and the magnetic confinement of electrons in the quantum-well wires leads to complicated binding energies of the hydrogenic impurity, and high magnetic fields significantly increase the binding energies of the hydrogenic impurity in the case of weak spatial confinement.