To understand the operation principle of the modular multilevel converter (MMC) deeply, it is necessary to study the harmonic characteristics of the MMC theoretically. Besides, the analytical harmonic formulas of the MMC are useful in designing the main circuit, reducing the losses and improving the waveform quality. Based on the average switching function and the Fourier series harmonic analysis, this paper deduces the analytical expressions for such electrical quantities as the arm voltage, the arm current, the capacitor voltage, the capacitor current and the circulating current of the MMC. Finally, a digital model of a 21-level MMC-HVDC system is realized in PSCAD/EMTDC. The results of the analytical expressions coincide with the simulation results, which verify the effectiveness and feasibility of the proposed analytical expressions.