For the prediction of shock waves induced from supersonic flows and propagation of acoustic waves, a numerical scheme of high-order and high-resolution accuracy with the shock-capturing capability is strongly recommended. In this paper, the way to improve the performance of monotonicity-preserving numerical scheme is introduced briefly. The usage of compact reconstruction and the properly modified limiter enhances the accuracy in a smooth region while maintaining the stability near flwo discontinuitie. For the application of present scheme, a simulation for three-dimensional supersonic jet noise is conducted. Near-field flows and acoustic waves are successfully calculated, and the data on the permeable surface is used for the prediction of noise at far-field using Ffowcs-Williams and Hawkings equation. The noise data between experiment and simulation shows a validity of the present scheme for the application of supersonic jet noise prediction.