This paper considers a three-terminal hybrid DC transmission system in which the rectifier station adopts line-commutated converter (LCC) while the inverter station adopts parallel two-terminal modular multilevel converter (MMC). The focus of this paper is on the improvement of ride-through capability of LCC AC system in the presence of a fault. A strategy for improving the fault ride-through capability based on local information is proposed. First, the mathematical models of different types of converters in a hybrid DC system are established, and the influence of AC faults at the sending end on the DC transmission system is discussed. Second, in the presence of a slight fault on the AC side of LCC, the current margin control is proposed for the load center side MMC2, where the MMC2 maintains the DC port current as the minimum allowable value. Third, if a serious fault on the AC side of LCC causes a significant AC voltage drop, it is proposed that the non-load center terminal MMC1 adopts voltage margin control. In addition, the MMC1 takes over the DC system voltage control so as to maintain MMC2 to absorb minimum power from the DC system, and prevent the load center connected by the MMC2 from removing too many important loads or causing a frequency collapse. Last, a large number of simulation results verify the effectiveness of the proposed methods.