The DC bipolar short-circuit is one of the most serious faults of DC grid, and the accurate calculation of postfault electrical stress will be meaningful for the system parameter design and protection setting. This paper proposes a calculation method of the short-circuit current under DC bipolar fault based on the discrete-time model of modular multilevel converter(MMC). Considering the discharge capacitors, the operating stages during one period can be obtained according to the number of submodules inserted into a bridge arm. Then, the accurate values of state variables can be calculated stage-by-stage using piecewise analysis. Finally, the MATLAB/Simulink simulation and experiment prototype of single-phase five-level MMC are established to verify the effectiveness and accuracy of the proposed method.