Data transmission based on the transmission matrix method has realized the multiplexing of a large number of orbital angular momentum (OAM) modes under scattering, which encodes the data by modulating the amplitude of the OAM modes. However, this amplitude modulation (amplitude encoding) method has obvious cross talk when the number of output modes is small, resulting in a non-negligible bit error rate. Here, a multi-channel data transmission method based on OAM phase modulation (phase encoding) under scattering is proposed. This method can resist the multiple-scattering effect of multimode fibers and realize accurate data transmission with very few rows of camera pixels for output mode measurement, which is suitable for high-speed data transmission under scattering. Experimentally, we have achieved a bit error rate of less than 0.005% in the data transmission of a color image through a 60 m multimode fiber with only 2 rows of camera pixels for output mode measurement. Experiments also showed that the proposed method has a higher stability than amplitude encoding when the proportion of "1" or "0" in the code changes.