In this work, the electrokinetic interactions between the undulated structure of an ion-selective membrane and electroconvective instability has been studied using numerical analysis. Using finite element method, electric fieldionic species transport-flow field were analyzed by fully-coupled manner. Through the numerical study, the Dukhin’s mode as the mechanism of undulated surface for the electroconvective instability were proven. The Dukhin’s mode which competes with Rubinstein’s mode has roles of (i) decreasing transition voltage to overlimiting regime and (ii) non-linearly increasing of overlimiting current. Also, (iii) the mixing efficiency is enhanced by removal mechanism of high-frequency Fourier mode of the electroconvective instability. Conclusively, the undulated ion-selective surface would provide energyefficient mechanism for ion-selective transport systems such as electrodialysis, electrochemical battery, etc.