In this work, we introduced a kind of new structured radial grating, which is named as even–type sinusoidal amplitude radial (ETASR) gratings. Based on diffraction theory and the principle of stationary phase, a comprehensive theoretical investigation on the diffraction patterns of ETASR gratings was conducted. Theoretical results show that novel carpet beams with beautiful optical structure and distinctive characteristics have been constructed on the basics of ETASR grating. Their diffraction patterns are independent of propagation distance, that is, the new carpet beams have diffraction–free propagating characteristics. The non–diffracting carpet beams are divided into two types by beam characteristic: non–diffracting integer order and half–integer order carpet beams. Subsequently, we experimentally generate these carpet beams by using ETASR grating. Finally, their particularly interesting optical morphology and features are explored through the numerical stimulations and experiment.