In order to describe and congnize the distribution of the diffraction field of axicon completely, according to the theory of asymptotic expansion, the diffraction integral function with large number and non-stationary end-point in integral domain is processed, the approximate analytical solution of intensity distribution in the shadow paraxial area of axicon is obtained, and a novel phenomenon that the distribution is Poisson diffraction spot is found. The experimental results show that the intensity distribution of diffraction spot follows zeroth-order Bessel function in shadow paraxial region, and the diffraction spot diameter increases linearly with the propagation distance, although its energy in longitudinal section has attenuation along with propagation. The illuminated beam and Poisson diffraction spot never overlap for both of their diameters increase linearly with propagation distance, so in theory this Poisson diffraction spot can be propagated to infinity. Compared with common methods, which through circular screen to generate Poisson diffraction spot, axicon provides a new convenient way for the production of Poisson diffraction spot in large-scale space.