To accelerate the electrons efficiently in the laser wake-field accelerator, it is necessary to suppress the instability induced by the diffraction and the defocusing of the laser pulse. The gas-filled capillary discharge waveguide can generate an approximately parabolic density distribution, which can guide the laser pulse efficiently and suppress the instability. Using the Stark effect, this plasma density distribution is measured in this paper, and the relationship between plasma density and filled pressure is presented. By using the MHD code CRMHA, the formation of the capillary waveguide is simulated and researched in detail.