A chain-increment method is developed to approach the chemical potential of a polymer with an all-atom model. The method relies on the structural feature that the polymer consists of repeated monomers, and the interactions with the surrounding molecules are introduced sequentially for the monomers in the tagged polymer. The solution theory in the energy representation is then adopted in combination with all-atom molecular simulations to compute the free energy of chain increment. This scheme identifies the incremented monomer as the solute and the surrounding molecules as the solvent, and the incremental free energy is obtained as a solvation free energy for the solute and solvent thus identified. The chain-increment method is applied to polyethylene (PE) in water and the polymer melts of PE, polypropylene, poly(methyl methacrylate), and poly(vinylidene difluoride). It is found for PE in water that the free energy of chain increment computed approximately by the energy-representation method stays constant within 0.2 kcal/mol except at a terminal and is in good agreement with the numerically exact one. The constancy of the incremental free energy is also seen for the polymer melts. The standard deviation is within 0.2 kcal/mol in the inner part of the polymer at the degree of polymerization of 100, and the averaged free energy of chain increment is insensitive to the chain length. This work demonstrates that all-atom computation is feasible for the free-energy analysis of a polymer system at the degree of polymerization of several tens or more.