The transmittance function of the axicon vertex off axis machining error is derived theoretically. Based on Huygens-Fresnel diffraction integral theory and stationary phase method, the expression of diffraction field behind the vertex off axis machining error is derived and the influence of the vertex off axis machining error in an axicon on the Bessel beams is analyzed. The expression of diffraction field behind the axicon is simulated numerically. Results show that if the axicon is ideal manufactured, the field distribution behind the axicon is approximately an ideal Bessel beam, and if the machining error exists, the diffraction beam pattern will split in half. At the same distance, the separation of the beam pattern will increase with the increasing of the vertex off axis machining error, with the same vertex off axis machining error, the separation of the beam pattern will increase with the increasing of the transmission distance. Meanwhile, the influence of the thickness of the element on the separation of the beam pattern is also studied. The results show that the separation degree of the beam pattern increases gradually with the increasing of the thickness. The findings offer some guidance for axicon machining and the application of Bessel beams, and so forth.