A method for producing a carbon fiber, comprising a step of dissolving or dispersing [I] a compound containing Co element; [II] a compound containing at least one element selected from the group consisting of Ti, V, Cr, and Mn; and [III] a compound containing at least one element selected from the group consisting of W and Mo in a solvent to obtain a solution or a fluid dispersion, a step of impregnating a particulate carrier with the solution or the fluid dispersion to prepare a catalyst, and a step of bringing a carbon source into contact with the catalyst in a vapor phase.