Abstract: In order to predict detectible range and region of passive sonar in underwater channel,an attenuation theory of envelope line-spectrum height for radiated noise of vessel in propagation and an approach of numerical prediction are proposed.In the paper a model for radiated noise of vessel is established by a periodically locally stationary random process,two formulae of the envelope line-spectrum height with background-noise and without backgroundnoise are deduced,therefore the attenuation rule of the envelope line-spectrum height is obtained,the result shows:the transmission loss of the sound level of the envelope line-spectrum is same as the sound level of the stationary spectrum, but the decrease of envelope line-spectrum height depends on a modified scale of amplitude modulation depth which is variable with the ratio of signal to noise.The numerical prediction approach as follows:first,the transmission loss of the stationary radiated noise is found out using the numerical approaches of normal modes or wavenumber integration or PE etc.,then the ratio of signal to noise on sound field is calculated,finally the decrease of envelope line-spectrum height is obtained according to the modified scale and the envelope line-spectrum heights in sound field can be predicted.The theory and the numerical prediction approach possess innovation,practicality,simplicity,suitability for engineering.