The orbital angular momentum (OAM) modes of electromagnetic (EM) beams are utilized for multiplexing in communication systems, where each OAM mode is encoded with data. The OAM index, or the so-called topological charge, identifies each OAM mode. Recently, the amplitude of OAM mode has also been used as another modulation format. Therefore, accurate extraction of not only the OAM index but also the corresponding amplitude is required. In this paper, a modified dynamic mode decomposition (DMD) algorithm is proposed to analyze the OAM modes. We show that accurate topological charges and high-resolution amplitude patterns of both single OAM mode and composite OAM modes can be obtained. This work offers an effective approach for demultiplexing OAM-carrying beams, especially when the high-resolution amplitude information is needed.