Based on linear potential flow theory, this study investigates the hydrodynamic performance of a horizontal cylinder wave energy converter (WEC) in front of a wall. The wall is assumed to be a partially reflecting vertical one, and the circular cylinder is fully submerged and restricted to only heave motion. The structural hydrodynamic quantities, including wave excitation force, added mass coefficient and radiation damping coefficient, are estimated using the well-known wide-spacing approximation, and the wave energy capture performance of the device is investigated. The estimation only requires solving the problems of water wave diffraction and radiation by a submerged horizontal cylinder in an open fluid domain, which can be analytically solved using the multipole expansion method. The estimation is validated by comparison with numerical results based on the boundary element method (BEM), and analytical results for the limiting case of a fully reflecting wall. Case studies are presented to clarify the effects of wave frequency, spacing between cylinder and wall, wall reflection and cylinder size on the hydrodynamic quantities and energy capture performance of the WEC. The hydrodynamic problem for regular waves is also extended to irregular waves. The results indicate that the WEC's performance can be significantly improved owing to the presence of a wall, which provides several feasible approaches for capturing more wave energy, such as setting vertical plates behind WECs and installing WECs near caisson breakwaters. This study also provides a reliable method for evaluating the performance of other WECs.