The surface tension of the full three-dimensional Lennard-Jones potential is calculated from grand canonical Monte Carlo simulations with the finite-size scaling methodology outlined by Binder [Phys. Rev. A 25, 1699 (1982)]. Surface tensions are determined for the range of reduced temperatures T*=0.95-1.312 and are found to be in good agreement with molecular-dynamics calculations. A critical temperature T-c*=1.311 +/- 0.002 is established by locating the T* where the surface tension of the infinite system size vanishes. In addition, with this method it is possible to determine the critical exponent 2 nu. For the Lennard-Jones fluid we found 2 nu=1.42 +/- 0.08, which differs from the accepted value of 2 nu=1.26. (C) 2000 American Institute of Physics. [S0021-9606(00)51014-9].