Electron density in a gas-filled capillary plasma for laser wakefield acceleration is a crucially important parameter for successful acceleration experiment. We measured the electron density by using the interferometric method, and some important plasma parameters such as an on-axis density and a channel depth are characterized with the discharge plasma current. The results from the interferometric method are also compared with the spectroscopic measurement results using the H-beta line for confirming their validity, and a reasonably good argeement is found between them.