The effect of non-linear phenomenon such as wave run-up and wave impact on the heaving buoy wave energy converter may lead to its efficiency decrease and overtopping. In this study, a hydrodynamic simulation of wave run-up heights and maximum wave loads on a cylindrical heaving buoy is constructed and preliminarily analysed using the Reynolds-averaged Navier–Stokes equations. The numerical results show that kinetic energy is mainly concentrated in the wave-ward and leeward sides of the buoy. Further, the maximum pressure at the bottom of the buoy occurs on the leeward side when the wave hits the buoy, increasing by 47% over the initial pressure and 32% over the maximum pressure at the centre of the buoy. For a heaving buoy with the power take-off mechanism (PTO), the damping coefficient is the main parameter that affects the wave run-up and wave loads. By contrast, for a heaving buoy without PTO, the wave height and the radius of the buoy are the main parameter. The accuracy of the numerical results is verified through model tests of the motion response of the buoy and the wave surface characteristics around it. The computational method can guide future buoy designs in terms of safety and reliability.