A method of producing a polymer includes hydrolyzing and condensing a hydrolyzable-group-containing silane monomer (B) in the presence of one or more polycarbosilanes (A), at least one of the polycarbosilanes (A) being a polycarbosilane (I) having a weight average molecular weight of 500 or more and obtained by reacting a compound of the following general formula (1) in the presence of at least one of an alkali metal and an alkaline earth metal, R.sup.1.sub.mY.sub.3-mSiCR.sup.2.sub.nX.sub.3-n (1) wherein R.sup.1 and R.sup.2 individually represent a monovalent organic group or a hydrogen atom, X represents a halogen atom, Y represents a halogen atom or an alkoxy group, and m and n individually represent integers from 0 to 2.