For future networks (i.e., the fifth generation (5G) wireless networks and beyond), millimeter-wave (mmWave) communication with large available unlicensed spectrum is a promising technology that enables gigabit multimedia applications. Thanks to the short wavelength of mmWave radio, massive antenna arrays can be packed into the limited dimensions of mmWave transceivers. Therefore, with directional beamforming (BF), both mmWave transmitters (MTXs) and mmWave receivers (MRXs) are capable of supporting multiple beams in 5G networks. However, for the transmission between an MTX and an MRX, most works have only considered a single beam, which means that they do not make full potential use of mmWave. Furthermore, the connectivity of single beam transmission can easily be blocked. In this context, we propose a single-user multi-beam concurrent transmission scheme for future mmWave networks with multiple reflected paths. Based on spatial spectrum reuse, the scheme can be described as a multiple-input multiple-output (MIMO) technique in beamspace (i.e., in the beam-number domain). Moreover, this study investigates the challenges and potential solutions for implementing this scheme, including multibeam selection, cooperative beam tracking, multi-beam power allocation and synchronization. The theoretical and numerical results show that the proposed beamspace SU-MIMO can largely improve the achievable rate of the transmission between an MTX and an MRX and, meanwhile, can maintain the connectivity.