PURPOSE: To easily obtain the subject polymer by hydrolytically condensing a dialkoxysilane with an aqueous acid solution, regulating the pH of the system with a metal oxide, and then removing the water and by-product alcohol.

CONSTITUTION: A dialkoxysilane (a) represented by the formula SiR1R2(OR3)2 [wherein R1 and R2 each is a (substituted)monovalent hydrocarbon group and R3 is methyl or ethyl] or a partial hydrolyzate thereof (b) is mixed with an aqueous acid solution having a pH of 1.0-5.0 to hydrolytically condense the compound (a) or (b), the amount of the acid being 0.5-3.0 times by mole the amount of the alkoxy groups of the compound (a) or (b). A metal oxide is added to the resulting reactional system to regulate the pH to 6.0-9.0, and the water and the alcohol formed as a by-product are removed.