In this paper, a LCC series-parallel resonant converter is designed for the electromagnetic launch system, in which, the power supply charges for the energy-storage capacitor in the Pulse Forming Unit. At first, the operational principles of the LCC resonant topology operating in Discontinuous-Current-Mode are analized and the detailed expressions describing the resonant topology are derived. In order to attain the Zero-Current-Switch characteristics in DCM, traditional pulse frequency modulation always restricts the up-band of switches operating frequency, this results in a decrease in output averaged current with the increase of PFU capacitor voltage. This affects the PFU charging efficiency greatly. While, it is an efficient way to solve this problem using the modulation of critical-DCM to extend frequency up-band, which can improve the duty ratio of the output current, ensure the charging efficiency. In this paper, an equivalent simplified linear function is developed to fit with the critical-DCM frequency one, so critical-frequency curve can be tracked online by using Digital-Signal-Processor. The duty ratio of the output current under critical frequency is improved greatly in contrast with traditional PFM. Moreover, in order to obtain a constant current output, a charging current-fed digital PID control scheme in DSP is designed for overcoming the input voltage disturbance and load disturbance. At last, the pictures of energy-storage capacitor charging supply and experiment figures are presented. Simulation and experimental results verify the analysis with good agreement. The designed power supplies realize ZCS soft-switching in the whole operating process, and at the same time, a constant output of charging current is obtained. The expected performance of 0-6kV charging voltage and 1A output current are achieved. The power supply group can be managed by the upper computer through CAN bus.