Twisted light carrying orbital angular momentum (OAM), which features a helical phase front, has shown its potential applications in diverse areas, especially in free-space optical (FSO) communications. Multiple orthogonal OAM beams can be utilized to enable high-capacity FSO communication systems. However, for practical OAM-based FSO communication links, atmospheric turbulence will cause serious power fluctuations and inter-model crosstalk between the multiplexed OAM channels, impairing link performance. In this paper, we propose and experimentally demonstrate a novel OAM mode-group multiplexing (OAM-MGM) scheme with transmitter mode diversity to increase system reliability under turbulence. Without adding extra system complexity, an FSO system transmitting two OAM groups with a total of 144 Gbit/s discrete multi-tone (DMT) signal is demonstrated under turbulence strength D/r0 of 1, 2, and 4. In our experiments, the proposed OAM-MGM scheme helps to achieve bit-error-rate (BER) mostly less than 3.8 × 10-3 under turbulence strength D/r0 of 1 and 2 with a total transmitted power of 10 dBm. Compared with the conventional OAM mode multiplexed system, the system interruption probability decreases from 28% to 4% under moderate turbulence strength D/r0 of 2.