We have explored the cohesive property of a monolayer of C (60) molecules (ML- C (60)) by means of total energy calculations with the density-functional theory. The total energy curve calculated for ML- C (60), which is obtained as a function of the lattice constant, has two minima and shows a hysteresis in the compression-tension stroke. These two minima in energy correspond to the different structural phases of ML- C (60): one is a monomer phase and the other is a polymer one. The energy band gap within the framework of the local density approximation varies from 1 eV (semiconducting phase) to 0 eV (metallic phase) with external pressure and without structural transition from the monomer phase to the polymer one.