A radio wave driven by Orbital angular momentum (OAM) is called a vortex radio and has a helical wavefront. The differential helical wavefronts of several vortex radios are closely related to their topological charges or mode numbers. In physics, two or more radio waves with different mode numbers are orthogonal to their azimuth angles. With the development of radio communication technologies, some researchers have been exploring the OAM-based multi-mode multiplexing (multi-OAM-mode multiplexing) technologies in order to enhance the channel spectrum efficiency (SE) of a radio communication system by using the orthogonal properties of vortex radios. After reviewing the reported researches of OAM-based radio communication, we find that some breakthroughs have been made in the combination of OAM and traditional Multi-Input-Multi-Output (MIMO). However, the existing technology is not sufficient to support OAM-based MIMO system to achieve maximum the channel SE. To maximize the spectrum efficiency of OAM-based MIMO system, we present a reused multi-OAM-mode multiplexing vortex radio (RMMVR) MIMO system, which is based on fractal uniform circular arrays (UCAs). The scheme described in this study can effectively combine multi-OAM-mode multiplexing with MIMO spatial multiplexing. First, we present the generation of RMMVR MIMO signals. Second, under line-of-sight (LOS) propagation conditions, we derive the channels of the RMMVR MIMO system. Third, we separate the RMMVR MIMO signals using an orthogonal separation method based on full azimuth sampling. Finally, we introduce the method for calculating the channel capacity of the RMMVR MIMO system. Theoretical analysis shows that the scheme proposed in this study is feasible. Moreover, the simulation results show that spatial and mode diversity are obtained by exploiting fractal UCAs. However, to enhance the channel SE of RMMVR MIMO system, an interference cancellation method needs to be introduced for zero-mode vortex radios, and some methods of multi-OAM-mode beams convergence and mode power optimization strategy should be introduced in the future.