Based on structures and characteristics of traditional hydraulic pumps, this paper proposes a novel high-temperature and high-pressure hydraulic pump (HHHP) that can work under 150°C and 28 MPa to overcome problems of traditional high-temperature plunger pumps. The HHHP is designed with the structure of mechanical division and double cylinder parallel. The control signals of two cylinders are two separate triangle waveforms with 90° phase difference. Because the output waveforms of two cylinders have the same characteristics as the control signals, the HHHP can obtain a stable output after two separate waveforms are superposed. A mononeuron self-adaptive PID control algorithm is also improved by modifying parameters K and η. Two improved controllers are used to control the two cylinders, respectively, making two displacements of plungers match each other. Therefore, reduced fluctuations and stable pressure output is obtained. Besides simulation, tests on the built prototype test system are carried out to verify the performance of HHHP. Results show that the improved control approach can limit fluctuations to a lower level and the HHHP system attains good outputs under different signal periods and different pressures.