A method for producing sizing agent-coated carbon fibers coated with at least one sizing agent selected from the group including the following [a], [b] and [c] wherein a di- or higher functional epoxy compound and/or an epoxy compound having mono- or higher functional epoxy groups and at least one or more types of functional groups selected from hydroxyl groups, amide groups, imide groups, urethane groups, urea groups, sulfonyl groups and sulfo groups are/is used as component, comprising the steps of coating carbon fibers with said sizing agent and heat-treating in a temperature range from 160 to 260°C for 30 to 600 seconds such that the deposited amount of the sizing agent is in a range from 0.1 to 10 parts by mass per 100 parts by mass of carbon fibers. [a] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a tertiary amine compound and/or tertiary amine salt with a molecular weight of 100 g/mol or higher used as component, with 100 parts by mass of the component [b] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a quaternary ammonium salt having a cationic moiety represented by either the following general formula or used as component, with 100 parts by mass of the component (where R 1 to R 5 denote, respectively independently, any one of a hydrocarbon group with 1 to 22 carbon atoms, a group containing a hydrocarbon with 1 to 22 carbon atoms and an ether structure, a group containing a hydrocarbon with 1 to 22 carbon atoms and an ester structure, and a group containing a hydrocarbon with 1 to 22 carbon atoms and a hydroxyl group; R 6 and R 7 denote, respectively independently, any one of a hydrogen, a hydrocarbon group with 1 to 8 carbon atoms, a group containing a hydrocarbon with 1 to 8 carbon atoms and an ether structure, and a group containing a hydrocarbon with 1 to 8 carbon atoms and an ester structure) [c] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a quaternary phosphonium salt and/or phosphine compound used as component, with 100 parts by mass of the component [a] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a tertiary amine compound and/or tertiary amine salt with a molecular weight of 100 g/mol or higher used as component, with 100 parts by mass of the component [b] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a quaternary ammonium salt having a cationic moiety represented by either the following general formula or used as component, with 100 parts by mass of the component (where R 1 to R 5 denote, respectively independently, any one of a hydrocarbon group with 1 to 22 carbon atoms, a group containing a hydrocarbon with 1 to 22 carbon atoms and an ether structure, a group containing a hydrocarbon with 1 to 22 carbon atoms and an ester structure, and a group containing a hydrocarbon with 1 to 22 carbon atoms and a hydroxyl group; R 6 and R 7 denote, respectively independently, any one of a hydrogen, a hydrocarbon group with 1 to 8 carbon atoms, a group containing a hydrocarbon with 1 to 8 carbon atoms and an ether structure, and a group containing a hydrocarbon with 1 to 8 carbon atoms and an ester structure) [c] A sizing agent obtained by mixing at least 0.1 to 25 parts by mass of a quaternary phosphonium salt and/or phosphine compound used as component, with 100 parts by mass of the component