The elastic property of a copper (Cu) thin film was investigated using the surface acoustic wave (SAW) measurement technique. The Cu film was deposited on a quartz substrate using a direct current magnetron sputter and its surface morphology was inspected using atomic force microscopy. Time-domain waveforms of the SAW on the film were acquired at different propagation distances to estimate the Young’s modulus of Cu such that the experimentally-obtained dispersion curve can be compared to the analytical result calculated using the Transfer Matrix method for curve-fitting. Results showed that the film’s elastic property value decreased by 18.5% compared to that of the bulk state, and the scale effect was not significant in the thickness range of 150-300 nm, showing good agreement with those by the nanoindentation technique. The property, however, increased by 15.5% with the grain coarsening.