Medium exchange of particles/cells to a clean buffer with a low background is essential for biological, chemical, and clinical research, which has been conventionally conducted using centrifugation. However, owing to critical limitations, such as possible cell loss and physical stimulation of cells, microfluidic techniques have been adopted for medium exchange. This study demonstrates a continuous on-chip washing process in a co-flow system using viscoelastic and Newtonian fluids. The co-flow system was constructed by adding a small amount of biocompatible polymer (xanthan gum, XG) to a sample containing particles or cells and introducing Newtonian fluids as sheath flows. Polymer concentration-dependent and particle size-dependent lateral migration of particles in the co-flow system were examined, and then the optimal concentration and the critical particle size for medium exchange were determined at the fixed total flow rate of 100 μL/min. For clinical applications, the continuous on-chip washing of white blood cells (WBCs) in lysed blood samples was demonstrated, and the washing performance was evaluated using a scanning spectrophotometer.