The diffractive axicon for the illumination with Gaussian beams is designed. The stationary phase method and the numerical calculation are used to analyze the diffraction integral describing the diffraction field. It is shown that with the Gaussian beam illumination of a smaller beam radius, the axicon can produces the uniform-axial-intensity with the lower oscillation frequency and the smaller oscillation amplitude. In addition, with the Gaussian beam illumination of a suitable beam radius, we can achieve the more uniform central-core width.