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This paper deals with the asymptotic synchronization of fractional-order complex dynamical networks with different structures and parameter uncertainties (FCDNDP). Firstly, the FCDNDP model is proposed by the Riemann–Liouville (R-L) fractional derivative. According to the property of fractional calculus and the Lyapunov direct method, an original controller is proposed to achieve the asymptotic synchronization of FCDNDP. Our controller is more adaptable and effective than those in other literature. Secondly, a sufficient condition is given for the asymptotic synchronization of FCDNDP based on the asymptotic stability theorem and the matrix inequality technique. Finally, the numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]