We present a novel flow-rate independent cell counter using a fixed control volume between double electrical sensing zones. The previous device based on the single electrical cell sensing in a given flow-rate requires an accurate fluid volume measurement or precision flow rate control. The present cell counter, however, offers the flow-rate independent method for the cell concentration measurement with counting cells in a fixed control volume of $22.9{pm}0.98{mu}{ell}$. In the experimental study, using the RBC (Red Blood Cell), we have compared the measured RBC concentrations from the fabricated devices with those from Hemacytometer. The previous and present devices show the maximum errors of $20.3\%;and;16.1\%$, which are in the measurement error range of Hemacytometer (about $20\%$). The present device also shows the flow-rate independent performance at the constant flow-rates ($5{mu}{ell}/min$ and $10{mu}{ell}/min$) and the varying flow-rate (4, 2, and $4{mu}{ell}/min$). Therefore, we demonstrate that the present cell counter is a simple and automated method for the cell concentration measurement without requiring an accurate fluid measurement and precision flow-rate control.