The present invention relates to a method for continuous production of carbon nanotubes in a nano-agglomerate fluidized bed, which comprises the following steps: loading transition metal compounds on a support, obtaining supported nanosized metal catalysts by reducing or dissociating, catalytically decomposing a carbon-source gas, and growing carbon nanotubes on the catalyst support by chemical vapor deposition of carbon atoms. The carbon nanotubes are 4.about.100 nm in diameter and 0.5.about.1000 .mu.m in length. The carbon nanotube agglomerates, ranged between 1.about.1000 .mu.m, are smoothly fluidized under 0.005 to 2 m/s superficial gas velocity and 20.about.800 kg/m.sup.3 bed density in the fluidized-bed reactor. The apparatus is simple and easy to operate, has a high reaction rate, and it can be used to produce carbon nanotubes with high degree of crystallization, high purity, and high yield.

 
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