A polyester polymer includes a dicarboxylic acid or its ester-forming derivative and a dihydroxy compound, in which the dicarboxylic acid contains an alicyclic dicarboxylic acid and optionally an aromatic dicarboxylic acid, and the dihydroxy compound contains a compound of formula (1): ##STR1## wherein R.sub.1 represents a C.sub.1-4 alkylene group; and R.sub.2, R.sub.3, R.sub.4 and R.sub.5 each represents a hydrogen atom, a C.sub.1-4 alkyl group, an aryl group or an aralkyl group which may be the same or different. Also, polyester moldings of disc substrates, lenses, sheets, films, tubes or fibers are produced by molding the polyester polymer. The polyester polymer has excellent transparency, excellent heat resistance, extremely low optical anisotropy and excellent moldability.