Based on the Fresnel diffraction theory, the influence of the vertex manufacture precision of an axicon on the light propagation is analyzed in detail. It is points out that the axicon is equal to a plano-convex lens for focusing the beams when the vertex is machined to a circle. However,the blunt-tip region of a real axicon can be described actually by a hyperbola, where the aberration non-diffracting beams will be formed due to the interference oscillation. This paper presents the theoretical derivations of diffractive fields from the axicon with different vertexes and analyzes and simulates their characteristics of beam propagation and transformation. Finally, a method for modifying the influence of a hyperbola-tip axicon is proposed to correct the interference effect and to obtain an approximate non-diffraction beam. It is shown that proposed method has guiding significance to the application of the real manufacture axicon.