Mode-division multiplexing over fibers has attracted increasing attention over the last few years as a potential solution to further increase fiber transmission capacity. In this paper, we demonstrate the viability of orbital angular momentum (OAM) modes transmission over a 50-km few-mode fiber (FMF). By analyzing mode properties of eigen modes in an FMF, we study the inner mode group differential modal delay (DMD) in FMF, which may influence the transmission capacity in long-distance OAM modes transmission and multiplexing. To mitigate the impact of large inner mode group DMD in long-distance fiber-based OAM modes transmission, we use low-density parity-check (LDPC) codes to increase the system reliability. By evaluating the performance of LDPC-coded single OAM mode transmission over 50-km fiber, significant coding gains of >4 dB, 8 dB and 14 dB are demonstrated for 1-Gbaud, 2-Gbaud and 5-Gbaud quadrature phase-shift keying (QPSK) signals, respectively. Furthermore, in order to verify and compare the influence of DMD in long-distance fiber transmission, single OAM mode transmission over 10-km FMF is also demonstrated in the experiment. Finally, we experimentally demonstrate OAM multiplexing and transmission over a 50-km FMF using LDPC-coded 1-Gbaud QPSK signals to compensate the influence of mode crosstalk and DMD in the 50 km FMF.