A lobed rotor-type pump has a drive shaft, a pump housing, an eccentric rotor journal, a rotor, three working-fluid chambers, intake and discharge ports, and a communication passage. The pump housing has a circumferentially-extending peri-trochoidal curved surface in its inner periphery. The eccentric rotor journal is fixedly connected to the drive shaft. The rotor is slideably fitted to the eccentric rotor journal. The rotor has three lobes equi-distantly spaced circumferentially around its outer periphery so that the rotor rotates eccentrically while keeping the lobes in sliding contact with the peri-trochoidal curved surface. The three working-fluid chambers, which are defined between respective three lobes and the peri-trochoidal curved surface, rotate in synchronism with the rotor. The intake and discharge ports are provided in the housing to input low-pressure incompressible fluid and to output high-pressure fluid. The communication passage is formed in the housing for communicating a first working-fluid chamber, decreasing in volume during the compression stage, and a second working-fluid chamber, increasing in volume during the expansion stage, to permit flow of incompressible fluid from the first chamber to the second chamber.