An orbital-angular-momentum (OAM) mode-group multiplexing (MGM) scheme using high-order mode groups (MGs) in a graded-index ring-core fiber (GIRCF) is proposed, in which a receive-diversity architecture is designed for each MG to suppress the mode partition noise resulting from random intra-group mode crosstalk. The signal-to-noise ratio (SNR) of the received signals is further improved by a simple maximal ratio combining (MRC) technique on the receiver side to efficiently take advantage of the diversity gain of the receiver. Intensity-modulated direct-detection (IM-DD) systems transmitting three OAM mode groups with total 100-Gb/s discrete multi-tone (DMT) signals over a 1-km GIRCF and two OAM mode groups with total 40-Gb/s DMT signals over an 18.4-km GIRCF are experimentally demonstrated, respectively, to confirm the feasibility of our proposed OAM-MGM scheme.