This work is focused on the characterization and magnetorheological (MR) study of MR fluids composed of iron particles and sepiolite fibers, used as a thickening agent. The work is aimed at (a) understanding the effect of the sepiolite addition on the MR response and (b) finding an appropriate formulation allowing a good sedimentation stability keeping a relatively low off-state viscosity and providing an enhanced MR effect. In the presence of an applied magnetic field, the composite MR fluid exhibits a yielding behavior with a progressive enhancement of the field-induced static yield stress with increasing volume fractions of both iron and sepiolite. Such an effect is attributed to a friction between gap-spanning aggregates composed of iron particles and sepiolite-oil viscoplastic matrix. The field-induced dynamic yield stress shows an initial increase with the sepiolite concentration (explained by a partial expulsion of the sepiolite fibers from the aggregates) followed by a decrease. The proposed mechanisms are supported by developed qualitative theoretical models, one of which is based on the homogenization approach of Chateau et al. [J. Rheol. 52, 489-506 (2008)]. From the practical point of view, the formulation containing 10 vol.% of iron and 4 vol.% of sepiolite seems to combine a perfect sedimentation stability with moderate values of the plastic viscosity and of the off-state static yield stress (only similar to 5 Pa) and with a relatively important static and dynamic yield stress enhancement (30% and 60%, respectively). (C) 2018 The Society of Rheology.