The generalization of combination– combination (C–C) synchronization of chaotic n-dimensional (nD) fractional-order (0 α ≤ 1) dynamical systems is studied. Firstly, we replace arbitrary four chaotic nD ordinary dynamical systems by four chaotic nD fractional-order dynamical systems which have unique solutions. Secondly, we extend the scheme of a recent paper (Sun et al. in Nonlinear Dyn 73: 1211–1222, 2013) to study the generalization of C–C synchronization among four nDfractionalorder dynamical systems. Examples of combination– combination synchronization among four identical or different of 6D chaotic fractional-order systems are discussed. The analytical formula of the control functions is tested numerically to achieve C–C synchronization, and good agreement is found