For the prediction of acoustic waves from rocket plume, over-expansion effects on Mach 3.0 supersonic jet acoustics are investigated with monotonically integrated large eddy simulation. In this study, ideally-expanded Mach number and designed Mach number are used to express the jet conditions. Three designed Mach number 3.0, 3.5 and 4.0 are chosen, while ideally-expanded Mach number is constant 3.0. Reynolds number is 100000 and coldjet condition is adopted to reduce computational costs. With regard to computation, the seventh order weighted compact non-linear scheme and the tenth order compact scheme are used for solving the jet-flow and near fields acoustics propagation, respectively. Computational results of Mach wave emissions of these three conditions are almost same. This result corresponds to that of relatively low Mach number supersonic which is reported by Tam(AIAA paper 2005-2938). Present results show that it can be applied to high Mach number supersonic jet. For the the prediction of acoustic waves from rocket plume, this results imply that rocket parameters could be reduced.