An original compressor for generating hydrogen high pressures (up to 4 kbar) in a 30 cm(3) volume at room temperature is described. The construction has no moving mechanical components and consists of two different parts. The first one is a metal-hydride thermo-sorptive compression module based on the hydride-forming material MmNi(5). Inlet pressure of the module is 1.5 MPa; discharge pressure is about 40 MPa. The second, cryogenic, part of the compressor consists of two cryo-stages that are designed as high-pressure containers of volume 60 and 30 cm(3) respectively. The cryogenic stages may be cooled to a temperature of 78 K and warmed to room temperature. At the lower temperature level in the cryo-stages, a hydrogen pressure of 40 MPa is generated by the hydride part of the compressor. Then, under consecutive heating-off of these two cryo-stages, the latter generates a pressure up to 400 MPa. A cycle period for generation of the maximal pressure is about 90 min. A combined construction of the compressor makes it possible to speed up significantly the process of hydrogen compression, to afford its high purity and at the same time to receive high pressure level in closed systems providing recovery of the working medium (hydrogen, deuterium, tritium) without any losses of the latter.