A three-dimensional numerical model developed based on the finite element method to simulate the position-reconstruction performance of multilayer capacitive anodes is presented. The charge collection efficiency and position nonlinearity are calculated for different electrode layers, patterns, and sizes, as well as the distance between the bottom microchannel plate (MCP) and induction layer. The position nonlinearity exhibits an approximately linear relationship with the electrode size and the distance between the bottom MCP and induction layer. By increasing the electrode area in the perimeter region and designing 2.2 mm square electrodes in the central region, a position nonlinearity of 3.36% with a distance of 5 mm between the bottom MCP and induction layer is achieved. The imaging performance of the six multilayer capacitive anodes is evaluated using a custom-designed detector prototype, and the experimental results validate the simulation results. The comprehensively optimized capacitive anode shows an imaging nonlinearity of 0.91% in the experiment. © 2024