The modular multilevel converter (MMC) has attracted significant interest for medium-/high-power energy conversion applications due to its modularity, scalability, and excellent harmonic performance. One of the technical challenges associated with the operation of the MMC is the circulation of double-frequency harmonic currents within its phase legs. This paper proposes a circulating current control strategy in a double-frequency rotating reference frame, which, contrary to the existing solutions that are based on approximate/inaccurate models, relies on an experimentally identified nonparametric model of circulating currents to determine the coefficients of the controller. Minimizing the squared second norm of the error between the open-loop transfer function of the system and a desired one, the coefficients of the controller are determined. To guarantee the stability of the closed-loop system, the minimization problem is subjected to a few constraints. The validity and effectiveness of the proposed control strategy is confirmed, and its dynamic performance is compared with that of an existing solution by experimental results.