The constant-NVT Monte Carlo simulation is performed for model C-60 molecules interacting via the Girifalco potential and a full free-energy analysis is made to predict the high-temperature phase diagram. The repulsive part of the C-60 potential is very steep and the attractive part is relatively short-ranged. For such a system accurate computations of the virial pressure are difficult in simulations and it is argued that the discrepancies among the previous results for the phase diagram of C-60 can partly be attributed to the uncertainties of the virial pressure involved in simulations. To avoid this difficulty we take the energy route to calculate equation of state (EOS), in which the absolute (Helmholtz) free energy is obtained by performing isochoric integration of the excess internal energy. A difficulty of the energy route in the high-temperature limit is resolved by the aid of an analytic method. The exact second and third virial coefficients are also used in the analysis of the fluid EOS. The pressure route is taken to calculate the EOS of the solid phase, in which the virial pressure is numerically more stable than in the fluid phase. The resulting high-temperature phase diagram of C-60 is quite systematic and free from uncertainties, and the liquid-vapor critical point is found at T-c=1980 K and rho(c)=0.44 nm(-3), whereas the triple point at T-t=1880 and rho(t)=0.74 nm(-3), confirming the existence of a stable liquid phase over the range of similar to 100 K.