Due to having a number of advantages, Marx generators are still the most widely used devices for generating high-voltage pulses in many fields of science and technology. To ensure their proper operation, especially when the generation of many frequent, highly repetitive pulses is required, a highly efficient high-voltage power supply is needed. The paper describes a specially developed power supply (input voltage 48 V DC, output voltage up to 50 kV) based on the conventional Full Bridge topology with two high-frequency high-voltage transformers and a 6-stage voltage multiplier. In order to avoid many problems caused by low coupling between primary and secondary windings of the transformers and the large parasitic capacitances of the secondary windings, a special quasi-resonant zero-current switching transistor control algorithm with variable switching frequency (dependent on output load) was developed. In the described method, the energy is supplied to the transformer in short pulses, when a pair of diagonal transistors of the full-bridge converter were turned on. Then, the freewheeling state is maintained until all of the energy stored in the leakage inductance of the transformer has been transferred to the secondary side, which means that the current in the primary windings drops to zero. This approach reduces energy losses, electromagnetic disturbances and prevents current distortion in primary winding.