This paper focuses on investigating a global maximum principle with recursive utilities, where the controlled state process is driven by a general mean-field FBSDE. In our setting the control domain is not necessarily convex, and the diffusion coefficient depends on control, as well as the generator of mean-field BSDE depends on the joint law of (X,Y). We adopt the method of the second-order variation and borrow the notion of the second-order derivative of a function with respect to a probability measure, to solve this optimal problem. By considering a new second-order variational equation and the corresponding second-order adjoint equation, a new second-order expansion of is established. Then the optimal principle is proved with this second-order expansion.

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