The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the nonlocal elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through the wave method and that in previous researches. The wave method is introduced to vibration analysis of the fluid-delivering carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the nonlocal elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. that, the critical flow velocity when the carbon nanotube loses stability is obtained. in previous researches.