As the structures of multiple branch lines (MBLs) will be widely applied in the future flexible DC distribution network, there is a urgent need for improving system reliability by tackling the frequent non-permanent pole-to-pole (P-P) fault on distribution lines. A novel fault restoration strategy based on local information is proposed to solve this issue. The strategy firstly splits a double-ended power supply network into two single-ended power supply networks through the timing difference characteristics of a hybrid direct current circuit breaker (HDCCB) entering the recloser. Then, a method based on the characteristic of the transient energy of fault current is proposed to screen the faulty branch line in each single-ended power supply network. Also, a four-terminal flexible DC distribution network with MBLs is constructed on PSCAD to demonstrate the efficacy of the proposed strategy. Various factors such as noise, fault location, and DC arc equivalent resistance are considered in the simulation model for testing. Test results prove that the proposed strategy for fault restoration is effective, and features high performance and scalability.