On the basis of the stationary phase method, a new diffraction-free carpet beam is generated. Specifically, the Fresnel diffraction of radial gratings after passing through the axicon is investigated by the stationary phase method, and under the approximate conditions of the stationary phase, a kind of carpet beams with the diffraction-free transmission characteristics is theoretically obtained. Then, the amplitude-based spatial light modulator (SLM) is adopted to load the radial gratings with different parameters, and the phase modulation element (axicon) is installed behind SLM. Upon the Fresnel diffraction, a new family of instances of diffraction-free carpet beams can be generated within a certain transmission range behind the axicon. Finally, it is found that the experimental results are in good agreement with the theoretical simulation results.