Monte Carlo calculations have been carried out for binary mixtures of Lennard-Jones model fluids in their supercritical fluid region. The molar excess enthalpies have been calculated for a total of twelve systems which have four different kinds of unlike interactions. One representative case is the system called LB-2-1 which was studied so far extensively as a model of nonpolar mixtures. It is found that excess enthalpies for LB-2-1 system in supercritical region are positive and remarkably larger in magnitude than those at high pressures (> 1000 atm) and at zero pressure/room temperature, and that molar composition dependence of excess enthalpy becomes highly asymmetrical. The present results are qualitatively the same with the tendency found in accurate calorimetric studies. Thermodynamic analysis has been performed to account for the present unique behavior in supercritical fluid region.