We have studied the reversal behavior in a single nanomagnet of CoPt by using anomalous Hall effect measurement technique. [Co (0.6-1.4 nm) Pt (2 nm)] 3 multilayer films were lithographically patterned into single dots with the diameter of 200 nm. The magnetic anisotropy Ku of the dots was varied from 1.3× 107 to 2.6× 107 ergcc by decreasing the Co thickness. From the rectangular magnetization curve and the Stoner-Wohlfarth-type angular dependence of reversal field, the magnetization reversal of the dot was concluded to proceed by the nucleation of a reversed embryo and its immediate expansion. The energy barrier Eb (0) for the magnetization reversal evaluated by the reversal probability experiment increased monotonically with Ku and showed the almost same dependence on Ku both at 300 and 100 K. These results suggest that the reversal mechanism is simply dominated by the magnetic anisotropy Ku and is invariable in this temperature range. This behavior of Eb (0) can be qualitatively explained by considering the nucleation of an embryo having the size of domain wall width.