The　underwater　noise　can　be　caused　by　the　radial　electromagnetic　vibration　of　permanent　magnet　synchronous　motor　(PMSM)　for　electric　propulsion.　The　difficulty　in　decreasing　the　underwater　noise　is　not　only　the　high-frequency　but　also　low-frequency　vibration　reduction.　This　paper　proposes　a　novel　random　asymmetric　carrier　pulse　width　modulation　(RACPWM)　method　for　PMSM　vibration　reduction　in　the　whole　frequency　range.　Instead　of　the　conventional　symmetric　triangular　carrier　PWM,　the　asymmetric　carrier　PWM　(ACPWM)　is　used　to　decrease　the　low-frequency　phase　current　harmonics　and　the　associated　low-frequency　vibration.　Meanwhile,　in　order　to　suppress　the　high-frequency　vibration,　the　RACPWM　control　based　on　the　amplitude　randomization　of　the　sawtooth　carrier　is　further　presented　to　reduce　the　high-frequency　phase　current　harmonics.　Moreover,　the　RACPWM　is　equivalent　to　the　random　slope　ACPWM　in　view　of　the　output　signals.　Furthermore,　without　the　need　of　any　additional　circuits　in　the　drive,　the　presented　method　is　simple　to　implement　by　software.　Simulation　and　experimental　results　show　that　the　proposed　RACPWM　method　can　effectively　reduce　both　the　low-frequency　and　the　high-frequency　vibration.