Integrating heat pump water heater (HPWH) into latent heat thermal energy storage (LHTES) with phase change material (PCM) has been recognized as a promising way to mitigate the energy use for heating water in the building sector. This paper uses zeotropic mixture R1234yf/R1234ze(Z) in HPWH and spherical PCM encapsulations in LHTES. The mathematical model is established and validated. Effects of zeotropic mixture composition, working fluid flow rate and heat transfer fluid (HTF) flow rate are discussed to reveal the instantaneous behaviors and overall performance of the integrated system. The results indicate that as the charging process progresses, the condensing pressure of the system steadily increases, leading to a decline in COP. By employing zeotropic mixtures, the system performance can be effectively improved, with the highest COP of 2.68 when the mass fraction of R1234ze(Z) is 70 %, which represents an 18.1 % and 6.8 % improved COP compared to R1234yf and R1234ze(Z), respectively. A smaller refrigerant flow rate or a larger HTF flow rate contributes to a higher COP. For heat storage capacity in LHTES, a higher mass fraction of R1234ze(Z) and a larger refrigerant flow rate are preferable, while a smaller HTF flow rate is beneficial. Finally, a multi-objective optimization is carried out. Results suggest that the best overall performance is achieved with a COP of 2.70 and a heat storage capacity of 629.24MJ, under conditions of the mass fraction of R1234ze(Z) at 70 %, a refrigerant flow rate of 0.28 kg/s, and an HTF flow rate of 0.46 kg/s.