We present a theoretical study of the electronic thermoelectric power of a semiconductor parabolic quantum well in a magnetic field. The case of a longitudinal magnetic field, with respect to the temperature gradient, has been considered. The calculations were carried out taking into account spin-splitting of the dimensionally quantized electronic energy levels. It has been shown that in the region of strong confinement the thermoelectric power decreases with increasing magnetic field, which is related to the downward shift of the lower Zeeman-split spin subband.