When a modular multilevel converter based high voltage direct current (MMC-HVDC) system operates under grid faults, there will be a phase difference between the grid voltage and the converter output. It can be caused by grid voltage phase shifting and the integration effect of the phase-locked loop (PLL) in the converter. The system may exhibit an undesirable transient process with expanded current which is harmful for the converter devices. In this paper, a transient current estimation method is proposed for the scenario of converter-grid phase difference caused by the frequency shifting of the grid side. A piecewise phase calculation model is established to determine the transient phase difference of the system. Then, according to the maximum phase difference calculated by the model, the system stability is assessed and the maximum value of system transient current can be estimated after comparing the maximum phase difference with the critical phase difference and π. Finally, the current estimation results are verified by detailed circuit simulations of a 21-level MMC-HVDC system built in PSCAD.