Incorporating current limiting control algorithm into the control of modular multilevel converter based high voltage direct current grid (MMC-HVDC-Grid) can effectively reduce the breaking current of DC circuit breaker and realize low cost DC fault protection. In this paper, the evaluation indexes are proposed, including DC fault current suppression rate, transient energy flow (TEF) suppression rate and breaking current of DC circuit breaker (DCCB) to quantitively evaluate the fault current suppression ability of the four typical current limiting control algorithms in current literature. Firstly, the mechanisms of the four current limiting control algorithms are analyzed, including adaptive current limiting control, new active current limiting control, current limiting control of circulating current suppressor and virtual impedance method. Finally, taking the four terminal MMC-HVDC-Grid with half bridge submodules as an example, the performance of these algorithms under pole-to-pole short circuit fault is comprehensively evaluated in terms of the proposed evaluation indexes. The simulation results show that the DC fault current suppression rate is 55.03%, and the breaking current of the DCCB is 9.3 kA by the adaptive current limiting control algorithm. Adaptive current limiting control algorithm is the highest DC fault current suppression rate and the smallest breaking current of DCCB with four of algorithms.