In order to investigate the influence of the surface deviation axicon on the propagation characteristics of the non-diffracting beam, three deviation models relative to the ideal, which are concave to the inner side, convex to the outer side and hyperbolic distribution of the apex of the axicon were established. The amplitude transmittance function was deduced, and the emergent light field and intensity distribution of plane wave through the three kinds of axicon lens was analyzed and simulated on the basis of Fresnel diffraction theory. The results show that the intensity of the light field decreases, the focal length is prolonged, the light field of the longitudinal section gradually diverges and the diameter of the center spot is gradually increased along the axis when the generatrix concave to the inner side. The intensity of the light field increases, the focal length becomes shorter, the longitudinal section of the light field gradually converges and the diameter of the center spot along the axial becomes smaller when the generatrix convex to the outer side. When the vertex of axicon is distributed in hyperbola, the light field oscillation intensifies, the field intensity and the focal depth are almost constant and the longitudinal section of the light field gradually diverges and then returns to uniform distribution. The study will provide a theoretical basis for analyzing the influence of the machining error of axicon lens on the propagation characteristics of non-diffracting beam, and has a reference significance for further supplementing the diffraction field theory of non-diffracting beam and broadening the range of its engineering application.