In this paper, a special gradient-index electromagnetically induced transparency medium is induced with a Gaussian control field, which can be realized in a four-level ⁸⁷Rb cold atomic cloud. Special directional self-imaging and imaging transforming properties are studied in this work. Simulated results show that a complex object can be imaged in the cold atoms, as the control field substituted with the elliptical Gaussian beam, then the self-imaging is directional, which has potental application in encryption.