This paper presents a mathematical model for the single-phase hybrid modular multilevel converter (MMC). Based on the model, the DC and fundamental AC components of the circulating current of the single-phase hybrid MMC are analyzed and their expressions are derived for the first time. Based on the analysis, a novel dual-loop circulating current control scheme is proposed for the single-phase hybrid MMC. The proposed control scheme can suppress the low-order harmonics of the circulating current without affecting the output current. Consequently, the total harmonic distortions and peak/root-mean-square values of the arm currents, the current/voltage stresses on the submodules (SMs), and the power loss of the MMC are all reduced. Moreover, the proposed control scheme can effectively balance the energy between the upper and lower arms of the single-phase hybrid MMC. Experimental results on a prototype of the single-phase hybrid MMC with three SMs per arm are provided to validate the effectiveness of the proposed circulating current control scheme.