Ion concentration polarization (ICP) is one of the essential important mechanisms for biomolecule preconcentration devices as well as a fundamental transport phenomenon found in electrodialysis, electrochemical cell, etc. The ICP triggered by externally applied voltage enables the biomolecular analyte to be preconcentrated at an arbitrary position by a locally amplified electric field inside the microchannel. Conventional preconcentration methodologies using the ICP have two limitations: uncertain equilibrium position and hydrodynamic instability of preconcentration plug. In this work, a new preconcentration method in the dead-end microchannel around cation exchange membrane was numerically studied to resolve the limitations. As a result, the numerical model showed that the analyte was concentrated at a shock front developed in a geometrically confined dead-end channel. Furthermore, the electrokinetic behaviors for preconcentration dynamics were analyzed by changing microchannel’s applied voltage and volumetric charge concentration of microchannel as key parameters to describe the dynamics. This work would provide an effective means for a point-of-care platform that requires ultra-fast preconcentration method.