Background and Objectives: There are two types of linear field momentum in the macroscopic electrodynamics: Minkowski momentum, and Abraham momentum. The first is conserved inside the uniform substance, the second is included into the momentum balance in relation to the center of energy. These two quantities must comply with two measures of photon momentum. Unfortunately, the ad hoc quantization of the Minkowski momentum in dispersive medium leads to the theoretical photon momentum, which differs from the observed momentum. To overcome the discrepancy, it was assumed that field quanta are polaritons in medium with dispersion, and the photon momentum is defined by momenta of these polaritons. Methods: This paper proposes another way to eliminate the inconsistency between experimental photon momentum and photon momentum in the ad hoc quantization scheme. The assumption about polaritons is not used in this approach. Results and Conclusion: It is shown that a generalization of Minkowski momentum formula is needed in the quantization scheme for а transparent dispersive medium. The factor that takes into account the dispersion should be used in the formula. This factor exactly the multiplier that translates the field energy density in nondispersive medium into the energy density in dispersive one. The proposed quantization scheme also applied to the case of materials with negative permittivity and permeability (left-handed media).