A mathematical model of a DC-DC converter with consideration of the discontinuous current mode is considered. It is assumed that the DC-DC converter operates within a variable-frequency electric drive and is used for connecting the supercapacitors unit to the direct current link of the frequency convertor. The operation modes, the mathematical description as well as the time diagrams of the corresponding DC-DC converter values with consideration of the discontinuous current mode features are presented. When building the mathematical model of the DC-DC converter, it is also required to consider the unique features of the frequency converter direct current link model, which in its turn has a significant impact on the system transient processes. In this context, the equations system, describing the transient processes in the frequency converter direct current link, is presented. The mathematical model equations system, the flow diagram as well as the simulation results of the DC-DC converter operation in the direct and discontinuous current modes are presented.