The new horizons for HVDC systems and their applications has intensified the research in HVDC protection systems. The HVDC circuit breakers (CB) has been the center of the protection systems with vacuum interrupters (VIs) showcasing a great potential for application as a part of HVDC-CBs. However, VIs still face the problem of arc-reignition with limited studies in this area. This paper tends to address this problem by investigating the impact of the parameters of VI and the shunt L-C branch upon the re-ignition occurrence during switching process. An HVDC testing system and VI-based HVDC-CB were modeled using ATP software. The testing included investigation of the impact of the rate of rise of dielectric strength (RRDS) of VI, the type of LC circuit either active or passive and its timing of injection. The results showed that active L-C circuits demanded a longer delay time before insertion to avoid re-ignitions and the increase in RRDS reduced the reignitions. The main contributions of this paper include; investigating the arc re-ignition in VI-based HVDC-CB; analyzing the combined effect of the VI and L-C parameters upon those reignitions and providing a co-relation between the re-ignition occurrence and these parameters. That co-relation is used to define the most suitable delay time for LC circuit to avoid re-ignitions. The co-relation shows that the delay time is inversely co-related to the RRDS and directly-correlated to active LC types with lower values for passive L-C. This was applied to the simulation results and showed agreement with that co-relation.