This paper presents molecular dynamics simulation results for excess properties of binary mixtures composed of two-center Lennard-Jones with point quadrupole (2CLJQ) molecules. The effect of quadrupole moment on excess properties of highly nonideal model mixtures has been investigated at a given temperature, k(B)T/epsilon(A) = 3.68, and pressure, P sigma(A)(3)/epsilon(A) = 2. Results are reported for excess enthalpy and excess volume along with density and internal energy of several mixtures as a function of quadrupole moment. Competition between the effects of molecular elongation and quadrupole moment on total and excess properties has been observed. We have illustrated the explicit effect of quadrupole moment on excess properties of three selected real mixtures, O-2/N-2, C2H4/C2H6 and C2H6/CO2, the components of which can be modeled adequately by 2CLJQ potential. The effect of quadrupole moment is found to be moderate in mixtures O-2/N-2 and C2H4/C2H6, but it is substantial in mixture C2H6/CO2. These simulation results are important to develop and test theories of highly nonideal molecular fluid mixtures.