A novel microfluidic design is proposed for extracting cell deformability under a stable local pressure. In conventional approaches, cell deformability is evaluated based on cell's velocity through a constriction channel where the cell is deformed due to geometrical constraints. A stiff cell would move slower due to a greater resistance generated from the deformation. The pressure driving the flow inside the microfluidic system is assumed constant everywhere all the time. However, the assumption is not exactly true since instant change of flow resistance happens while a cell passing through the constriction. Such pressure change could affect the evaluation results, and should be suppressed as much as possible. In this work, we firstly investigate how such cell appearance affecting the local flow resistance and pressure change with theoretical modeling. After that, we proposed and fabricated a new microfluidic design to overcome such pressure variation. Two parallel channels are placed above and below the constriction channel, and the purpose is to reduce the resistance change due to cell appearance inside the constriction. Human red blood cells are tested, and the results give that the absolute correlation between cell size and velocity significantly improved from 0.42 to 0.63. The increased correlation physically makes sense because greater deformation causes a greater resistance which lowers cell velocity more. Therefore, the experimental results show that the proposed design effectively improves the cell evaluation from conventional approaches.