A fractional frequency transmission system (FFTS) is a promising solution to offshore wind power integration, for which the hexagonal modular multilevel converter (Hexverter) is an attractive choice for power conversion. The Hexverter has recently been proposed to directly connect two three-phase systems of different frequencies and voltage amplitudes, with only six branches in the FFTS in that case. This paper examines for the first time the control scheme of the Hexverter when applied to offshore wind power integration via a FFTS. Firstly, the frequency-decoupled mathematical model of the Hexverter is deduced by introducing the double dq transformation. Then the branch energy of the Hexverter is analyzed in detail and the reactive power constraint equation is obtained. The corresponding control scheme is thoroughly discussed, including the inner loop current control, the outer loop voltage control in both grid-connected mode and passive mode, and a novel optimization method to minimize the circulating current in the Hexverter. Finally, a simulation model of offshore wind power integration via a 4-terminal FFTS based on the Hexverter is built in MATALB/Simulink to verify the feasibility of Hexverter and the effectiveness of the control scheme proposed in this paper.