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The heaving wave energy converter (WEC) is one typical type of point absorber WECs with high energy conversion efficiency but significantly affected by the viscous effect. It is widely known that the bottom shape of such WECs plays an important role in influencing the viscosity, so a detailed qualitative investigation is essential. Here a numerical study is performed for the influence of bottom shape on motion response and energy conversion performance of a heaving WEC. The numerical model is developed based on the potential flow theory with a viscous correction in the frequency domain. Cylindrical WECs with flat, cone, and hemispherical bottoms and the same displacement are considered. WECs with larger diameter-to-draft ratios (DDRs) are found to experience a relatively smaller viscous effect and achieve effective energy conversion in a broader frequency range. With the same DDR, the flat bottom has the most considerable viscous effect, following by the cone bottom with conical angles 90° and the hemispherical bottom. When the DDR is relatively small, the hemispherical bottom had the best energy conversion performance. Similarly, when the DDR is relatively large, the energy conversion performance of the floater with a hemispherical bottom and a cone bottom with 90° is better, while that with the flat bottom is the worst.