The invention shows a production method for carbon nanotubes. The production method comprises a first step of feeding at least one kind of gas-phase catalyst into a first chamber, the at least one kind of gas-phase catalyst being formed from an iron family element-containing substance and a halogen-containing substance that are contained in a first liquid; and a second step of forming the carbon nanotubes from a carbon source fed into the first chamber using a catalyst generated based on the gas-phase catalyst existing in the first chamber, wherein the first step includes vaporization of the first liquid, and the first liquid does not contain the carbon source.