AC (alternating current) system backup protection setting calculation is an important basis for ensuring the safe operation of power grids. With the increasing integration of modular multilevel converter based high voltage direct current (MMC-HVDC) into power grids, it has been a big challenge for the AC system backup protection setting calculation, as the MMC-HVDC lacks the fault self-clearance capability under pole-to-pole faults. This paper focused on the pole-to-pole faults analysis for the AC system backup protection setting calculation. The principles of pole-to-pole faults analysis were discussed first according to the standard of the AC system protection setting calculation. Then, the influence of fault resistance on the fault process was investigated. A simplified analytic approach of pole-to-pole faults in MMC-HVDC for the AC system backup protection setting calculation was proposed. In the proposed approach, the derived expressions of fundamental frequency current are applicable under arbitrary fault resistance. The accuracy of the proposed approach was demonstrated by PSCAD/EMTDC (Power Systems Computer-Aided Design/Electromagnetic Transients including DC) simulations.