Abstract-This paper proposes a fast, selective, reliable and local bus primary relaying algorithm for high voltage direct current (HVDC) grids. The proposed relaying algorithm only uses measurements obtained from current sensors to detect faults and identify their locations. This algorithm is local and requires only communication at the bus level rather than system level. Furthermore, the algorithm is not sensitive to system configuration and operating point and can be employed during line or converter outages with limited re-tuning and adjustments.The proposed algorithm is applied to a four-terminal HVDC grid. Study results show that the proposed algorithm i) detects faults on both transmission lines and DC buses, ii) identifies the faulted bus or transmission line, iii) requires insignificant computation capacity, iv) distinguishes between faults and other system transients to prevent erroneous circuit breaker trips, and v) is not sensitive to measurement noise.