Abstract: Fractional frequency transmission system (FFTS) combines the advantages of HVAC and HVDC transmission system, thus it is a very promising solution for large-scale offshore wind power transmission. Modular multilevel matrix converter (M³C) which enjoys advantages of high power quality and easy scalability has attracted much attention in offshore FFTS. However, the input side and output side of M³C are directly coupled with different frequencies, which brings challenges to its modeling and control. To address this issue, a hybrid modeling method and the corresponding control strategy were proposed for M³C in this paper. The proposed method applied differential-common-mode modeling to the subconverters in order to realize the decoupling of input and output. Besides, αβ 0 modeling was applied to the arm power of each subconverter, which revealed the relationship between the fundamental component of the differential-mode current and the low-frequency component of the arm power. Based on the hybrid modeling, a novel system control strategy of M³C-FFTS was proposed, in which the positive sequence active component, negative sequence active and reactive components of the differential-mode current were utilized to realize capacitor voltage balancing. The constructed differential-mode current only contained the input frequency components, which significantly simplified the design of the controller. The effectiveness of the proposed modeling and control strategy was verified by a 220kV, 400MW M³C system implemented in Matlab.