The DC bipolar short-circuit is one of the most serious faults of DC grid, and the accurate calculation of post-fault 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.