This paper focuses on the global Mittag-Leffler boundedness for fractional-order fuzzy quaternion-valued neural networks (FOFQVNNs) with linear threshold neurons. In order to avert the non-exchangeability for quaternion multiplication, the considered QVNN is separated into four real-valued or two complex-valued systems. By employing Lyapunov function method and fractional-order differential inequalities, several effective conditions according to algebraic inequality and complex-valued linear matrix inequalities (LMIs) are deduced to guarantee the global Mittag-Leffler boundedness of the addressed network. And, the frame of the global Mittag-Leffler attracting sets (GMLASs) is presented as well. Here, the numbers of the equilibrium points need not to be concerned. Finally, a numerical example is provided to demonstrate the correctness of the proposed results.