An attempt is made to derive an expression for the effective electron mass along the direction of a magnetic field in bismuth under magnetic quantization by using the generalized dispersion relation of the conduction electrons as proposed by Meclure and Choi. It is found that the oscillatory quantum number dependent behaviour of the effective electron mass at the Fermi level in bismuth is solely due to band non-parabolicity and is a characteristic feature of the above model. © 1986, Verlag der Zeitschrift fur Naturforschung. All rights reserved.