A 3-D lumped parameter circuit model based on the nodal analysis to simulate signal propagation and position response characteristics of capacitive division image readout (C-DIR) is proposed. The current pulses, charge collection efficiency, and position reconstruction patterns are calculated for different electrical parameters (charge division capacitor C-c, perimeter capacitor C-p, diagonal capacitor C-d, electrode parasitic capacitor C-s, and the sheet resistance of the resistive layer R-Ge), and their influence on imaging linearity is investigated. The simulation results show that R-Ge affects the amplitude, pulsewidth, and polarity of the current pulse in the C-DIR. The sheet resistance of the resistive layer needs to be larger than 10 MQ for the charge to be efficiently collected by the readout electronics. Several capacitance ratios (C-c/C-p, C-c/C-s, and C-c/C-d) mainly affect the imaging linearity. It has been found that to obtain good detector imaging performance, C-c/C-p should be less than 0.01, C-c/C-s should be larger than 100, and C-c/C-d should be larger than 10, and when RGe is larger than 10 Mg, the imaging nonlinearity (rms) can be less than 1%. The reliability of the simulation results was verified by experimental measurements of a prototype C-DIR detector designed by ourselves. An optimized imaging performance with imaging nonlinearity (rms) of 2.18% was achieved.