Ion concentration polarization (ICP) has been widely applied in microfluidic systems in pre-concentration, particle separation, and desalination applications. General ICP microfluidic systems have three components (i.e., source, ion-exchange, and buffer), which allow selective ion transport. Recently developed trials to eliminate one of the three components to simplify the system have suffered from decreased performance by the accumulation of unwanted ions. In this paper, we presented a new ICP microfluidic system with only an ion-exchange membrane-coated channel. Numerical investigation on hydrodynamic flow and electric fields with a series of coupled governing equations enabled a strong correlation to experimental investigations on electroconvective vortices and the trajectory of charged particles. This study has significant implications for the development and optimization of ICP microfluidic and electrochemical systems for biomarker concentration and separation to improve sensing reliability and detection limits in analytic chemistry.