Based on Mei’s potential function, the pressure effect on elastic properties of Au are calculated by molecular dynamics method in the pressure range of 0~100 GPa. By fitting the Birch-Murnaghan equation of state, the pressure derivative of bulk modulus B0′ was obtained of 5.3. The calculation shows that the strength and rigidity of Au are enhanced by compression. The Zener anisotropy factor decreases with pressure, but within the considered range of pressure, elastic anisotropy still keeps large. The acoustic anisotropy factor is not sensitive to pressure, which means that the ratio of two longitudinal elastic wave velocities propagating along [100] and [111] direction is almost unchange.