The oscillating water column (OWC) converter, a prominent and widely adopted device for capturing wave energy, has yet to attain commercialization due to its intricate hydrodynamic behavior. Consequently, numerous laboratory and numerical studies have been carried out on OWC converters. One of the significant parameters in the study and comparison of different converters is their hydrodynamic efficiency parameter. Hence, the primary objective of this study is to examine the efficiency of an oscillating water column converter using the meshless method of fundamental solutions (MFS) to solve the governing equations. To address the challenges posed by the low wave steepness and to optimize computational efficiency, a complete linearization of two nonlinear sources at the boundary conditions inside and outside the OWC chamber was undertaken. Next, the boundary conditions were temporally discretized using three distinct methods: the Newmark, the forward differentiation formula, and the Runge-Kutta method of the fourth order. Subsequently, a comparison was made among these methods, revealing that the Newmark method exhibited a higher convergence rate to the solution. Using the developed numerical model, a more precise examination of the converter's efficiency, under various sloped bottom geometries, was conducted, surpassing the level of accuracy achieved in prior studies. Two key parameters, namely the opening, and slope, were identified as critical factors influencing the efficiency of converters considering sloped bottoms. The results indicated that the efficiency of the converter decreases with an increase in the slope and a decrease in the opening. Furthermore, to effectively interpret the efficiency of the converter, a suitable parameter was introduced the disparity in the free surface elevation inside and outside the chamber. This parameter proved valuable in providing insights into the converter's performance.