The influence of diameter of the Mo single-crystal nanowires on their strength for the three crystallographic orientations [100], [110] and [111] at temperatures of 77 and 300 K is revealed by means of the use of molecular-dynamic simulations. The existence of size effect in samples with diameter less than 4 nm is discovered. For cylindrical nanospecimen with the [100] orientation, size effect consists in the increase of strength by 17% with sample diameter decreasing from 4 to 1 nm. At the same time, when these nanospecimens are stretched along the [110] and [111] directions, an anomalous size effect is observed that manifests itself in a strength decreasing up to 14%. As shown, the reason for existence of these opposite tendencies in the manifestation of size effect is formation of different types of defects in nanosize specimens, namely, non-equilibrium twins under tension along the [100] direction and non-equilibrium dislocations under tension along the [110] and [111] directions.