A method for manufacturing carbon nanotubes comprising the steps of: mixing a clear aqueous metal solution with an alumina support, wherein the clear aqueous metal solution is prepared by sequentially mixing multicarboxylic acid and an aqueous catalytic component precursor solution with an aqueous active component precursor solution, wherein the addition order is such that the multicarboxylic acid is added to the active component before the catalyst component is added; vacuum drying the resulting mixture at 40 to 80°C and then baking the mixture at 650 to 800°C to obtain a two-component carbon nanotube catalyst in which a catalytic component and an active component are impregnated in and coated on the surface and micropores of the alumina support; adding the two-component carbon nanotube catalyst to a fluidized bed reactor and injecting at least one carbon source selected from C1-C4 saturated or unsaturated hydrocarbons, or the carbon source and a mixed gas of hydrogen and nitrogen into the reactor at 500 to 900°C; and growing non-bundled and spherical bulk shape carbon nanotubes on the surface of the two-component carbon nanotube catalyst, wherein the catalyst component is at least one selected from Fe salts, Fe oxides, Fe compounds, Ni salts, Ni oxides and Ni compounds and active component is Mo salt, Mo oxide or a Mo compound, and wherein the alumina support (Al 2 O 3), the catalyst component, the multicarboxylic acid and the active component are selected such that the number of moles (x) of the catalyst component and the number of moles (y) of the active component satisfy 34≤x≤46, 2≤y≤9 and 40≤x+y≤53, based on 100 mol of the alumina support. mixing a clear aqueous metal solution with an alumina support, wherein the clear aqueous metal solution is prepared by sequentially mixing multicarboxylic acid and an aqueous catalytic component precursor solution with an aqueous active component precursor solution, wherein the addition order is such that the multicarboxylic acid is added to the active component before the catalyst component is added; vacuum drying the resulting mixture at 40 to 80°C and then baking the mixture at 650 to 800°C to obtain a two-component carbon nanotube catalyst in which a catalytic component and an active component are impregnated in and coated on the surface and micropores of the alumina support; adding the two-component carbon nanotube catalyst to a fluidized bed reactor and injecting at least one carbon source selected from C1-C4 saturated or unsaturated hydrocarbons, or the carbon source and a mixed gas of hydrogen and nitrogen into the reactor at 500 to 900°C; and growing non-bundled and spherical bulk shape carbon nanotubes on the surface of the two-component carbon nanotube catalyst, wherein the catalyst component is at least one selected from Fe salts, Fe oxides, Fe compounds, Ni salts, Ni oxides and Ni compounds and active component is Mo salt, Mo oxide or a Mo compound, and wherein the alumina support (Al 2 O 3), the catalyst component, the multicarboxylic acid and the active component are selected such that the number of moles (x) of the catalyst component and the number of moles (y) of the active component satisfy 34≤x≤46, 2≤y≤9 and 40≤x+y≤53, based on 100 mol of the alumina support.