In　power　ultrasonic　and　underwater　acoustic　fields,　the　ultrasonic　treatment　efficiency　of　vibration　system　can　be　improved　significantly　when　vibration　system　is　driven　by　the　multi-frequency　longitudinal　transducer,　and　the　performance　of　vibration　system　is　determined　by　the　multi-frequency　characteristics　of　transducer.　In　this　paper,　using　electromechanical　equivalent　circuit　method,　the　multi-frequency　characteristics　of　a　longitudinal　ultrasonic　transducer　with　a　stepped　horn　are　studied　for　the　ultrasonic　vibration　system　optimal　design.　The　expressions　of　the　input　impedance　and　the　velocity　amplification　ratio　of　the　transducer　are　obtained.　The　relationships　between　the　electromechanical　coupling　coefficients,　the　velocity　amplification　of　the　multi　frequency　transducer　and　the　excitation　position　of　the　piezoelectric　stack,　the　size　of　the　stepped　horn　are　analyzed.　Combined　with　the　finite　element　analysis　of　the　transducer＇s　key　performance,　the　optimal　design　parameters　of　the　multi-frequency　transducer　are　given.　Finally,　the　electromechanical　properties　of　the　multi　frequency　transducer　are　tested　experimentally,　the　theoretical　analysis　and　finite　element　results　are　verified　well.