• A faster and effective method for seeking the optimal discharge pressure is proposed. • The pinch point characteristics in the gas cooler are comprehensively revealed. • The relationship between the pinch point and the optimal discharge pressure is clarified. • The thermal matching and COP are no longer related at high inlet water temperatures. • The performance differences between the CO 2 heat pump and R134a are clarified. The pinch point in the gas cooler significantly impacts the optimal discharge pressure and system performance of the CO 2 heat pump water heater, however the pinch point characteristics are still not fully revealed. Given this, a comprehensive thermodynamic investigation is conducted. The thermodynamic model is developed and validated, and a faster and effective method for seeking the optimal discharge pressure is proposed and proven accurate. The pinch point variation pattern with working conditions and its influence on the system performance are investigated. Besides, a comparative study on the CO 2 heat pump water heater with R134a is conducted under variable working conditions. The results show that there are four pinch point variation patterns. The pinch points may appear at the hot end, the interior, and the cold end of the gas cooler. At low inlet water temperature and large temperature lift conditions, two pinch points appear exactly at the optimal discharge pressure and are at the interior and the cold end. The appearance of the two pinch points enables the optimal thermal matching of CO 2 and water, resulting in a maximum coefficient of performance (COP). The two pinch points are still possible at high inlet water temperatures; however, the thermal matching and COP are not closely related anymore. The CO 2 heat pump water heater is more competitive than R134a for low inlet water temperature and large temperature lift conditions, but not vice versa. The results obtained may be helpful for the optimization and efficient control of the CO 2 heat pump.