The multi-terminal flexible DC grid line protection based on the characteristics of line boundary elements is hard to apply to the power grid when a current limiting reactor is installed at the outlet of the converter station. Thus a multi-terminal flexible DC grid line protection scheme based on low frequency transient energy ratios of the different outgoing lines of the converter station is proposed. First, through analyzing the impedance frequency characteristics of an MMC on the DC side after a fault, it is concluded that the MMC exhibits an inductive characteristic when the actual frequency is greater than the resonant frequency. Then through analyzing the variation rule of the voltage traveling wave refractive index at the bus with frequency is analyzed, we conclude that the low-frequency components with frequencies greater than the resonant frequency have obvious attenuation characteristics after being refracted by the bus. Then the difference in the low-frequency transient energy ratio of different outgoing lines of the converter station during forward and reverse faults is analyzed based on this conclusion. The fault direction can be determined via this difference. Finally, simulation results of PSCAD/EMTDC show that the proposed protection scheme can reliably identify fault directions without relying on line boundary elements, and it has a certain ability to withstand transition resistance.