The present invention provides a novel narrow distribution dendrimer-like star polymer having a controlled molecular structure, and a method capable of easily producing the star polymer. Disclosed is a polymer comprising a core portion and an arm portion, wherein the arm portion includes a first generation composed of a polymer chain and a second generation composed of a polymer chain formed at the outer shell of the first generation, the number of arms of the second generation is larger than the number of arms of the first generation, the first generation composed of the polymer chain is a polymer chain derived from a monomer having a polymerizable double bond, and the ratio of the weight average molecular weight (Mw) to the number average molecular weight (Mn), (Mw/Mn), of the star polymer is within a range from 1.001 to 2.50. A compound containing a functional group capable of reacting with an anion, which serves as a core portion, is reacted with a polymer chain containing two or more functional groups and an anion end which serves as an arm portion.