Abstract: Using measures adopted in fluid mechanics, a numerical method of noisereduction in duct with flow by anti-sound is established,in which a mathematical anti-soundmodel is deduced strictly. Several numerical examples are given out in cases of backward andforward sound propagation to illustrate the influence of anti-sound on sound field in duct andto discuss the effects of intensity,phase angle of anti-sound sources and flow velocity. It isshown that noise reduction by anti-sound dose have a bright prospect in engineeringapplication.