Constant pressure hydraulic power take-off (CPHPTO) utilizes a high-pressure accumulator to weaken its oil pressure fluctuations. However, CPHPTO operating point still changes violently under the circumstance of the changeable irregular waves as well as the limited volume of the high-pressure accumulator. This causes CPHPTO to work away from the designed operating point and even to run in the inefficient and unstable region. This paper proposes a speed-and-pressure combined control (SPCC) strategy, which keeps system speed/pressure around the designed value via the vector control of a PMSG or the displacement tuning of a hydraulic motor, for the efficient and stable operation of a CPHPTO. A SPCC strategy for the CPHPTO embedded in a novel inverse pendulum wave energy converter (NIPWEC) is designed in detail. Furthermore, the overall wave-to-wire dynamic model is simulated in irregular waves to research the effect of SPCC. Results show that both the SPCC with an oil pressure open-loop regulator (OPOLR) and the SPCC with an oil pressure closed-loop regulator (OPCLR) can effectively stabilize the system speed/pressure. Besides, SPCC, especially the SPCC with OPCLR, can effectively improve both the efficiency and stability of CPHPTO. Moreover, system-speed control is more significant than system-pressure control in terms of improving CPHPTO efficiency.