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 Hc2|c(T) increases quasi-linearly with decreasing temperature, the ab-plane Hc2|ab(T) shows a flattening, starting near 25 K above 30 T. This leads to a non-monotonic temperature dependence of the anisotropy parameter \gamma= Hc2|ab/Hc2|c. The anisotropy parameter is ~ 2 near Tc ~ 32 K and rises to a maximum \gamma ~ 3.6 around 27 K. For lower temperatures, \gamma decreases with T in a linear fashion, dropping to \gamma ~ 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.