In this article we report on the experimental investigation of light storage for several types of diffraction-free beams(Bessel and Airy beams)and quasi-diffraction-free beams by utilizing electromagnetically induced transparency(EIT)technique in a hot atomic gas cell.The experimental results show that the diffraction-free and quasi-diffraction-free beams have better storage performances when compared with ordinary images possessing similar spatial profiles.Meanwhile,the Bessel beams and the quasi-diffraction-free images are able to maintain their spatial profiles with a long storage time while the side-lobes of the Airy beam are gradually depleted with the increment of the storage time.We quantitatively analyze the storage results and give physical explanations behind these phenomena.Furthermore,the self-healing of the retrieved diffraction-free beams is verified,signifying that their characteristics preserve well after storage.