The high-voltage direct current (HVDC) grid has been recognized as an effective solution for renewable energy integration. Currently, two main development trends for HVDC grids are being studied: a DC breaker based HVDC grid and fault-blocking converter based HVDC grid. Although the former has a perfect performance for fault clearance, its development is still highly constrained by the cost and maturity of DC breakers. The latter can extinguish DC faults by the fault-blocking converters. Without using DC breakers, there is no bottleneck in its technical feasibility. Nevertheless, in fault scenarios, such types of HVDC grids will be blocked at length for air-deionization, which is its main drawback. The aim of this paper is to minimize its power interruption time, by optimizing protection coordination strategies. To cover the most complex cases, the overhead line applications, in which the reclosure actions are required to be implemented, are considered. In this paper, the protection requirements of HVDC grids are first discussed, then the benefits of fault-blocking modular multilevel converters (MMCs) and their fault features are analyzed. Based on this, a control function is designed to reduce the air-deionization time. To minimize the influence of the DC faults, a separation methodology for restarting the system is proposed. The effectiveness of the proposed protection coordination schemes is validated by PSCAD/EMTDC simulations.