The invention provides preparation and application of a supported cobalt sulfide catalyst for selectively synthesizing carbon nanotubes. The experimental process comprises the following steps: (1) preparing a silicon dioxide loaded cobalt sulfide catalyst, namely preparing the silicon dioxide loaded cobalt sulfide catalyst from pure cobalt sulfide and a silicon dioxide carrier through the treatment modes of infiltration, dispersion, heating and stirring, drying, grinding and the like; and (2) researching the condition that the silicon dioxide loaded cobalt sulfide catalyst which takes ethanolas a carbon source and has the cobalt content of 1-10 wt% catalyzes the growth of the carbon nanotubes by adopting a chemical vapor deposition method under the conditions that the reduction temperature is 600-900 DEG C, the growth temperature is 900 DEG C and the temperature rises at the heating rate of 10 DEG C/min. The silicon dioxide loaded cobalt sulfide catalyst prepared by the method can beused for selectively synthesizing single-walled carbon nanotubes and multi-walled carbon nanotubes with narrower tube diameter distribution by a chemical vapor deposition method.