A new method for calculating thermodynamics of any square-well systems by umbrella sampling of the corresponding hard-sphere systems is proposed. The removal of energetic barriers leads to an efficient configurational sampling. As an illustrative example, the method is applied to a square-well chain of freely-jointed 64 beads. Results indicate that it produces fast and more accurate thermodynamic results than either the direct molecular dynamics simulation or the umbrella sampling of the square-well chain. The new method, which provides a new route for accurate heat-capacity and free energy calculations, can be easily extended to a system interacting with the Lennard-Jones or any other continuous potentials.