Quasi-uniform synchronization of delayed fractional-order memristor-based neural networks (FMNNs) is discussed in this paper. On the basis of the theory of fractional differential equations and the theory of differential inclusion, the synchronization error system between the concerned drive system and the associated response system is formulated, and then, by employing Hölder inequality, C_p inequality and Gronwall-Bellman inequality, several sufficient criteria are proposed to ensure the quasi-uniform synchronization for the considered delayed FMNNs. Three simulation examples are also presented to illustrate the availability and correctness of the theoretical results.