Short-circuit faults are hazardous for high-power modular multilevel converters (MMCs). Hence, an accurate current calculation will be helpful to the system protection design. In this paper, a new method of short circuit current calculation based on a discrete-time modeling is proposed. With a commonly adopted nearest level modulation, the operating state during one period can be divided into several stages, according to the number of inserted sub-modules in a bridge arm. Then, a piecewise analysis allows to construct a new discrete-time model by recursion in the state variables stage-by-stage. From this model, the current evolution during short-circuit fault can be accurately calculated when given an initial state. The effects of different fault occurrence times in one period are also calculated and discussed. Finally, PSCAD/EMTDC simulations and a circuit experiment on a single-phase five-level MMC verify the effectiveness of the proposed calculation method.