Structural phase behavior of a thermotropic polyester, poly(hexamethylene 4,4＇-biphenyl-dicarboxylate), abbreviated as BB-6, was studied under hydrostatic pressures up to 200 MPa by wide-angle X-ray diffraction apparatus equipped with a high-pressure vessel. The C alpha form of BB-6, cooled slowly from the melt under atmospheric pressure, is the most stable in the low-pressure region below 70 MPa, and this sample exhibits the reversible phase transition of C alpha <-> S-A <-> I. An application of high pressure above about 100 MPa induces another crystal polymorph (C delta) at high temperature: the C alpha --> C delta --> S-A --> I transition process is observed on heating under high pressure. Since the C delta <-> S-A <-> I transition occurs reversibly at high pressure, the C delta form can be regarded as the stable form in the high-pressure region. But this form becomes metastable in the low-pressure region because the C delta --> C alpha --> S-A --> I transition is observed at pressures below 50 MPa. The shrinkage of the fiber repeat of the C delta form by about 2 Angstrom would suggest the conformational change from all-trans to an introduction of gauche (g+ or g-) conformation in the aliphatic sequence. Since the X-ray fiber photograph of the C delta form shows intense fiber reflections along the direction tilted by 25 degrees from the equatorial line, the molecular chains in the unit cell would be arranged in a herringbone pattern. The phase stability between the crystal modifications of BB-6 was analyzed as s function of temperature and pressure.