A method for producing a polymer includes hydrolyzing and condensing (B) a hydrolyzable-group-containing silane monomer in the presence of (A) a polycarbosilane, the polycarbosilane (A) being a polymer (I) obtained by reacting (a) a compound shown by the following general formula (1) and (b) at least one compound selected from the group consisting of a compound shown by the following general formula (2) and a compound shown by the following general formula (3) in an organic solvent in the presence of at least one of an alkali metal and an alkaline earth metal, R.sup.1.sub.kCX.sub.4-k (1) R.sup.2.sub.kSiY.sub.4-k (2) R.sup.3.sub.mY.sub.3-mSiCR.sup.4.sub.nX.sub.3-n (3) wherein R.sup.1 to R.sup.4 individually represent a monovalent organic group or a hydrogen atom, X represents a halogen atom, Y represents a halogen atom or an alkoxy group, k represents an integer from 0 to 3, and m and n individually represent integers from 0 to 2.