Method for producing soluble cross-linked polymer

[Problem] To provide a method for producing a soluble cross-linked polymer that is highly compatible with coating compositions, and that satisfactorily reduces pimple defects on a coating film when used as an additive. [Solution] A monomer A having two or more radical polymerizable double bonds per molecule is polymerized in a first organic solvent in the presence of a polymerization initiator B in an amount of 5 mol% to 200 mol% per mole of the monomer A,at a temperature that is at least 20˚C higher than the 10-hour half-life temperature of the polymerization initiator B, without refluxing.