The anisotropic upper critical field, Hc2(T), curves for K0.8Fe1.76Se2 are determined over a wide range of temperatures down to 1.5 K and magnetic fields up to 60 T. Anisotropic initial slopes of Hc2 ~ −1.4 T/K and −4.6 T/K for magnetic field applied along c axis and ab plane, respectively, were observed. Whereas the c axis Hcc2 (T) increases quasilinearly with decreasing temperature, the ab plane Habc2(T) shows a flattening, starting near 25 K above 30 T. This leads to a nonmonotonic temperature dependence of the anisotropy parameter γH≡ Habc2/Hcc2. The anisotropy parameter is ~2 near Tc~32 K and rises to a maximum γH~ 3.6 around 27 K. For lower temperatures, γH decreases with T in a linear fashion, dropping to γH~2.5 by T~18 K. Despite the apparent differences between the K0.8Fe1.76Se2 and (Ba0.55K0.45)Fe2As2 or Ba(Fe0.926Co0.074)2As2, in terms of the magnetic state and proximity to an insulating state, the Hc2(T) curves are remarkably similar.