A method is proposed for calculating the free energy of a fluid by a Monte-Carlo (MC) simulation based on a modified free-volume theory. With this method, it is possible to calculate the excess entropy over that of the ideal gas, and the internal energy, separately with one simulation at a given density and temperature, without a reference system other than the ideal gas. A radial free-space distribution function (RFSDF), ζ( r), is defined as the average of the Boltzmann probabilities of random displacements r of the molecules; this is a characteristic function for describing the nearest-neighbor molecular structure or the space in which a molecule can move. The function is obtained, effectively, as the ratio [(number of acceptances of displacement r)/(number of trials of displacement r), in a Metropolis MC simulation. The free volume is then computed by integrating ζ( r) with respect to the radial volume element 4π r 2d r. While the partition function of the system is obtainable from the free volume, the excess entropy is calculated here directly from the ratio of the free volume of the fluid to that of an ideal gas. The internal energy is obtained in the same runs by the usual Metropolis MC procedure. The excess entropy and/or the excess free energy agree very well with the values obtained from the equations of state for both the hardsphere system and the Lennard-Jones fluid.