A novel polymerization catalyst for polyesters, which does not contain any germanium or antimony compound as the main component; polyesters produced with the catalyst; and a process for producing polyesters. This polymerization catalyst is excellent in catalytic activity, little causes thermal degradation of polyesters in melt molding even when neither deactivated nor removed, and can give thermally stable polyesters which little generate foreign matter and are excellent in transparency and color. The polymerization catalyst is one which contains as the first metal-containing component at least one member selected from the group consisting of aluminum and aluminum compounds and which gives polyethylene terephthalate (PET) having a thermal stability parameter (TS) satisfying the relationship: (1) TS<0.3.