For the nearby dwarf star α Cen B (K1 V), we present limb-darkening predictions from a 3D hydrodynamical radiative transfer model of its atmosphere. We first compared the results of this model to a standard Kurucz's atmosphere. Then we used both predictions to fit the new interferometric visibility measurements of α Cen B obtained with the VINCI instrument of the VLT Interferometer. Part of these new visibility measurements were obtained in the second lobe of the visibility function, which is sensitive to stellar limb-darkening. The best agreement is found for the 3D atmosphere limb-darkening model and a limb-darkened angular diameter of θ 3D = 6.000 ± 0.021 mas, corresponding to a linear radius of 0.863 ± 0.003 R (assuming π = 747.1 ± 1.2 mas). Our new linear radius agrees well with the asteroseismic value predicted by Thévenin et al. (2002, A&A, 392, L9). In view of future observations of this star with the VLTI/AMBER instrument, we also present limb-darkening predictions in the J, H, and K bands.