In recent years, the azimuthal mode, also known as orbital angular momentum (OAM), and the radial mode of Laguerre Gaussian (LG) beam have been applied in many disparate areas of physics. Identification of them is the basic technique for these applications. Although there are many recognition methods, each has its own problems. Either it can only be used to distinguish one of OAM and radial modes, or the number of modes that can be distinguished is too small, or the operation is too complex. So, a great challenge is to design a method that is not only simple, but also applicable to the identification of both OAM and radial modes with a high dimension. Here, by introducing the strong mode selectivity, we propose a convenient method for identification of OAM and radial modes based on multiplexing holography. In our method, only a single hologram is need. Experiment on the identification of 100 OAM modes (l = –50, –49, …, +49, +50) has been carried out and demonstrates the feasibility of our design. What’s more, our method is also applicable to the identification of radial modes, and then to the identification of LG modes. In experiment, we have realized the identification of 8 radial modes (p = 1, 2, 3, …, 8) and 120 LG modes (p = 1, 3, 5, and l = –20, –19, ..., +20). Our method should have important applications in high-capacity optical communication based on OAM modes, radial modes, and/or LG modes.