By adopting the newly proposed two-Yukawa function [Y. Tang, Z. Tong, B.C.-Y. Lu, An analytical equation of state based on the Ornstein-Zernike equation. Fluid Phase Equilibria 134 (1997) 21-42] and our general solution of the Ornstein-Zernike equation for mixtures, an analytical expression in terms of the Laplace transform is obtained for the radial distribution function of LJ mixtures. The expression is found to be in good agreement with computer simulation data. Subsequently, an analytical equation of state (EOS), which is an extension of our recent EOS of the pure LJ fluid [Y. Tang, Z. Tong, B.C.-Y. Lu, An analytical equation of state based on the Ornstein-Zernike equation. Fluid Phase Equilibria 134 (1997) 21-42], is obtained for LJ mixtures. One powerful advantage of the new EOS is that it can be implemented in a simple analytical manner, and is free of integration. By comparing with computer simulation data, the EOS is found to predict very satisfactorily some typical thermodynamic properties of mixtures, including pressure, excess free energy, and chemical potential at infinite dilution. The predictions are also found to be better than the van der Waals one-fluid theory and to be overall better than two perturbation theories proposed recently.