Coarse-grained models for protein simulations can potentially access longer time scales in larger protein systems than atomic-level models. Here, a coarse-grained residue pair potential, with distance and orientation dependency, is derived from equilibrium ensembles of residue pairs generated by molecular dynamics (MD). In particular, the Boltzmann inversion method is used to determine the energies. The residue pair potential is combined with local dihedral angle potentials for the backbone and side chains and used in the folding simulations of six small proteins, (28-67 residues) containing a variety of secondary structures. For the proteins tested, folding simulations by Monte Carlo methods generate structures similar to the native ones. However, these native-like structures were among the lowest in energy for a helical proteins but not for proteins containing extended beta structures. It is also found that a careful balance between local and nonlocal interactions is essential. Possibilities for improving coarse-grained models derived from atomic force fields are discussed.