The experimental investigation on generation of fractional Bessel beams by focusing the fractional vortex beams with an axicon is carried out. It is shown that when the fractional vortex beams are focused by the axicon, the transverse intensity distribution of the fractional Bessel beams possesses characteristics of high order non-diffracting Bessel beams. Within the maximum collimating distance behind the axicon, the focused light spots seem unchanged during propagation. The fractional Bessel beams have a very good characteristics of non-diffraction. Moreover, the influence of cone angle of the axicon on the fractional Bessel beams is investigated. The experimental results show that the bigger the cone angle of axicon is, the smaller the central hollow of the transverse intensity distribution is.