As　an　internal　excitation　form,　oscillation　attenuation　flow　significantly　affects　the　stability　and　resonance　characteristics　of　fluid-conveying　pipeline.　Here,　based　on　the　differential　equation　of　transverse　vibration　of　pipeline　conveying　fluid,　the　exponential　attenuation　function　was　introduced　to　simulate　oscillation　attenuation　characteristics　of　flow　velocity　when　water　hammer　happening,　and　the　expression　of　dynamic　instability　region　of　pipeline　conveying　fluid　under　the　action　of　internally　excited　oscillation　attenuation　flow　was　derived.　Under　the　condition　of　unattenuated　periodic　pulsating　flow　excitation,　the　unsteady　regions　of　two　kinds　of　pipelines　with　different　supports　were　calculated,　they　were　in　good　agreement　with　the　previous　numerical　results　published.　Meanwhile,　compared　with　the　velocity　time　history　calculated　using　viscoelastic　pipe　model　under　water　hammer,　it　was　shown　that　the　proposed　velocity　expression　can　better　reflect　bidirectional　attenuation　characteristics　of　flow　in　the　pipeline　under　water　hammer　excitation.　Furthermore,　the　influence　of　attenuation　characteristic　parameters　on　the　unstable　region　of　simply　supported　pipeline　was　analyzed.　The　results　showed　that　the　influence　of　the　internally　excited　oscillation　attenuation　flow　on　the　transverse　vibration　of　the　pipeline　can＇t　be　ignored;　when　the　flow　velocity　attenuation　coefficient　b　increases,　the　unstable　region　moves　downward,　and　when　the　initial　flow　velocity　u0　increases,　shifting　phenomenon　becomes　more　obvious;　at　the　same　time,　with　passage　of　time　and　increase　in　attenuation　coefficient　b,　the　faster　the　flow　velocity　attenuation　and　the　faster　the　closure　of　unstable　region;　when　flow　velocity　attenuation　reaches　0,　water　hammer　process　is　over,　unstable　area　of　pipeline　disappears.　©　2021,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.