A method for producing a polymer by using the living radical polymerization initiator, represented by the following general formula: in the formula, R 1 represents an organic group which is linkable with two or more other organic groups, and is selected from an aliphatic group having 1 to 12 carbon atoms, an aromatic group, an alkylcarbonyl group having 1 to 12 carbon atoms, an alkoxycarbonyl group having 1 to 12 carbon atoms, an aminocarbonyl group, an alkylaminocarbonyl group having 1 to 12 carbon atoms, a dialkylaminocarbonyl group having 1 to 12 carbon atoms, an arylcarbonyl group, an alkylsulfonyl group having 1 to 12 carbon atoms, an aryl sulfonyl group, and an organic group in which two or more of those groups are combined, R 2, R 3, R 4 and R 5 are a hydrogen atom or an organic group selected from an aliphatic group having 1 to 12 carbon atoms, an aromatic group, an alkylcarbonyl group, an alkoxycarbonyl group, an aminocarbonyl group, an alkylaminocarbonyl group, a dialkylaminocarbonyl group having 1 to 12 carbon atoms, an arylcarbonyl group, a carboxy group, an alkylsulfonyl group having 1 to 12 carbon atoms, and an aryl sulfonyl group, X and Y are a halogen atom, m and n are an integer of 1 or more, and the X and Y are in a state in which they are different from each other in reactivity with a monomer; the method comprising: a first polymerization step in which, for only one halogen atom of the X or Y of the living radical polymerization initiator, a living radical polymerization reaction in which the living radical polymerization reaction initiator is mixed with a monomer with unsaturated bond and the reaction is carried out at a reaction condition depending on a type of the monomer one or more times while changing in order the type of the monomer to be mixed to obtain a first product; and a second polymerization step in which, for both halogen atoms of the X and Y contained in the first product, at least one type of the monomer is subjected to a living radical polymerization reaction in order at a reaction condition depending on a type of the monomer to obtain a final product. in the formula, R 1 represents an organic group which is linkable with two or more other organic groups, and is selected from an aliphatic group having 1 to 12 carbon atoms, an aromatic group, an alkylcarbonyl group having 1 to 12 carbon atoms, an alkoxycarbonyl group having 1 to 12 carbon atoms, an aminocarbonyl group, an alkylaminocarbonyl group having 1 to 12 carbon atoms, a dialkylaminocarbonyl group having 1 to 12 carbon atoms, an arylcarbonyl group, an alkylsulfonyl group having 1 to 12 carbon atoms, an aryl sulfonyl group, and an organic group in which two or more of those groups are combined, R 2, R 3, R 4 and R 5 are a hydrogen atom or an organic group selected from an aliphatic group having 1 to 12 carbon atoms, an aromatic group, an alkylcarbonyl group, an alkoxycarbonyl group, an aminocarbonyl group, an alkylaminocarbonyl group, a dialkylaminocarbonyl group having 1 to 12 carbon atoms, an arylcarbonyl group, a carboxy group, an alkylsulfonyl group having 1 to 12 carbon atoms, and an aryl sulfonyl group, X and Y are a halogen atom, m and n are an integer of 1 or more, and the X and Y are in a state in which they are different from each other in reactivity with a monomer; a first polymerization step in which, for only one halogen atom of the X or Y of the living radical polymerization initiator, a living radical polymerization reaction in which the living radical polymerization reaction initiator is mixed with a monomer with unsaturated bond and the reaction is carried out at a reaction condition depending on a type of the monomer one or more times while changing in order the type of the monomer to be mixed to obtain a first product; and a second polymerization step in which, for both halogen atoms of the X and Y contained in the first product, at least one type of the monomer is subjected to a living radical polymerization reaction in order at a reaction condition depending on a type of the monomer to obtain a final product.