The paper considers an opportunity of soft-starting of frequency converters input AC-DC unit using a controlled rectifier instead of the diode one, where the control angle of thyristors during the process of starting is continuously decreasing. Thus the voltage of the capacitor loaded through the limiting reactor is constantly increasing. The mathematical description of the process is given in the paper and realized with some assumption. The parameters of network current pulses and voltage of the capacitor have been approximately described with mathematical expressions within an n-th time interval considering the changes of the input voltage during the pulse time linear and assuming that the capacitor voltage negligibly changes within one pulse influence. The modeling of the transient processes in the considered system has been realized with the help of PSIM software. The highest peak of the amplitude of the current was investigated depending on the duration of the starting. The increasing of the starting time leads to the maximum current amplitude decreasing. The absolute value of the network current i1 , voltage of the capacitor uc and control characteristics are demonstrated in the article. The characteristics after the computer modelling have been presented together with those calculated theoretically. The results were compared and evaluated for the accuracy.