This paper is concerned with the robust state estimation problem for a class of delayed fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with norm-bounded uncertainties. The objective of the study is to construct an efficient estimator in such a way that the behavior of the corresponding error state is stable in the Mittag-Leffler sense. Distinct to the previous studies, the state estimation problem of FOBAM NNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global Mittag-Leffler stability of the error system are derived as a set of solvable linear matrix inequalities (LMIs) without uncertainties. The proposed stability conditions are further extended to the FOBAM NNs by considering the effect of uncertainties. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated. © 2020 The Franklin Institute