The phase transition of a thermotropic (4,4’-dihydroxybiphenylyl)tetradecanedionic acid polyester (PB-12) was studied using wide-angle X-ray scattering and differential thermal analysis (DTA) under hydrostatic pressures up to 300 MPa. The corrected T vs P phase diagram of the PB-12 polyester was constructed by a high-pressure DTA method. The typical phase transition of crystal (K)-smectic H (S-H)-isotropic melt (I) was observed under hydrostatic pressures up to 90-100 MPa. At high pressures above about 100-120 MPa, however, a new smectic phase, clearly different from the usual S-H phase, is found at high temperatures and a different transition process of K-new smectic phase-I can be observed at elevated pressures. The new smectic phase is also formed irreversibly from the usual S-H phase by increasing pressure on a quasi-isothermal process. The pressure-induced smectic phase was assigned to be a smectic B (S-B) phase because the d spacing of the low-angle reflection corresponds to the extended length of the PB-12 molecule, suggesting the arrangement of the molecules vertical to the smectic layer, and also a single reflection at the wide-angle region, suggesting a hexagonal packing. The S-B phase was partly supercooled at high pressures, and the glassy S-B phase coexistent with the normal crystals was analyzed under atmospheric pressure.