Support-mesh structures of a self-supporting transmission grating may decrease the transmission area and diffraction efficiency, thus exert a ill effect on the original diffraction pattern of the grating and make it complicated to apply, especially in soft X-ray region. To solve this problem, we put forward a method to realize a kind of totally self-supporting transmission grating by arranging the rectangular transmission holes in a high Z foil quasi-randomly. Based on Fraunhofer's diffraction theory, we make a theoretical analysis on the diffraction pattern of this new kind of grating. We also calculate the diffraction pattern of this new kind of grating based on the Kirchhoff's diffraction theory. What's more, we fabricated a sample grating of 1000 lines/mm using focused ion beam (FIB) technology and then tested it on beam line 4B7B on the Beijing synchrotron radiation facility. Theatrical analysis and experimental result both proved that the diffraction of the transmission grating can get rid of the bad influence of the support-mesh structures by using this new designed method. Such a methodology can profit applications of this kind of X-ray dispersive element in a wide field.