We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around 0.94-1.20, and temperatures ranging from 0.1 to 2.0 (values in reduced Lennard-Jones units). The absolute free energy at an arbitrary state point in this range is obtained by integrating over density and temperature from the triple-point. Our result for the free energy is in very good agreement with the values reported in literature previously. Also the melting line obtained from our free energy expression, in combination with an equation of state for the liquid phase, is in excellent agreement with results by Agrawal and Kofke [Mol. Phys. 85, 43 (1995)] obtained via the Gibbs-Duhem integration method.