Abstract: Abundant dynamic effects on an ion-selective surface provide a new solution for the development of microfluidic technology. If an increasing bias voltage is applied to the electrolyte solution with the ion-selective surface, the passing ion current will experience a complex nonlinear evolution. A convection phenomenon will be triggered when the imposed voltage exceeds a critical threshold. This convection is called the electroconvection near the ion-selective surface or the second kind of electroosmosis. The numerical investigation of the electroconvection attracted a number of studies. In the present work, a numerical model of the lattice Boltzmann method (LBM) based on multi-block grid refinement is proposed to simulate this model problem. The grid information exchange equations of the multi-block grid refinement method for solving the flow, potential, and ion concentration are given, which overcomes the requirement of a high concentration gradient boundary for the computational resolution. The current-voltage characteristic curve obtained by the numerical model firstly increases rapidly with the increase of voltage and then reaches a saturation state. This result is in good agreement with the theoretical solution. What is more, the results also show that after the convection occurs, the flow tends to form large rolls under a relatively low voltage which is slightly higher than the stability threshold, and the flow intensity increases exponentially. While under a relatively high voltage, multiple small rolls are formed firstly, and these rolls merge into larger rolls subsequently. The ion transport efficiency is higher when the large rolls are formed. It is worth noting that our multi-block LBM method is suitable not only for the electric convection on the ion-exchange surface but also for some other numerical studies of electrohydrodynamics.