A new type of axicon is proposed for generating quasi long-distance non-diffracting beams. This new type of optical element is grinded to a concave spherical surface on the bottom of a traditional axicon. The formation of the long-distance non-diffracting beams is analyzed by the theory of geometrical optics. Its amplitude transmissivity function is derived. The intensity distribution of plane wave pass through the concave axicon is simulated by diffraction theory. The results show that the appropriate radius of curvature of axicon can produce long-distance non-diffracting beams with low divergent and good uniformity. Take an axicon with base angle γ of 10°, refraction index n of 1.51509 and curvature radius R of 75 mm for example, the maximum non-diffracting distance Zmax of 471.220 mm is obtained when radius of the incident beam a is 10 mm, while the traditional axicon with the same base angle and refraction index can obtain non-diffracting distance of 111.235 mm. The non-diffracting distance increases by 359.985 mm.