Pool boiling is the heat-transfer mechanism of many heat exchangers inside ocean nuclear power plants working under the complex marine circumstances. Also, ocean conditions will create a new acceleration field other than gravity for the fluid, which induces some unique thermal–hydraulic characteristics. In this study, pool boiling under heaving conditions is numerically simulated using multiple relaxation time phase change lattice Boltzmann method. Firstly, the simulated results under static condition have been validated with recognized empirical equations, such as Rohsenow’s correlation at nucleate boiling, Zuber’s model, and Kandlikar’s model about critical heat flux (CHF). Then, pool boiling patterns, the boiling curve of time-averaged heat flux, transient heat flux, and heaving effects on different pool boiling regions are investigated. The results show that pool boiling curves of time-averaged heat flux between heaving conditions and static conditions with middle superheat degrees are similar. Heat transfer under heaving conditions at low superheat is somewhat enhanced, and it is weakened at high superheat, which leads to a slightly smaller critical heat flux with larger superheat compared with that under static conditions. Moreover, distinct fluctuation of the transient heat flux of pool boiling under heaving conditions is found for all boiling regimes. Furthermore, the heaving condition shows both positive and negative effects on pool boiling heat transfer at high-gravity and low-gravity regions, respectively. Besides, both the larger heaving height and shorter period time bring out more violent heaving motion and make a greater impact on pool boiling heat transfer.