Phase behavior of four homologues compounds of optically isotropic, thermotropic cubic mesogens 1,2-bis-(4-n-alkyloxybenzoyl)hydrazine, BABH(n), n indicating the number of carbon atoms in the alkyloxy chain, was investigated under pressures up to 300MPa using a high-pressure differential thermal analyzer, a wide-angle X-ray diffractometer and a polarizing optical microscope equipped with a high-pressure optical cell. The transition sequence for BABH(8) and BABH(10), low-temperature crystal (Cr-2)-high-temperature crystal (Cr-1)-cubic (Cub)-smectic C (SmC)-isotropic liquid (1) observed under atmospheric pressure, is held in the low pressure region below about 30MPa and 10MPa, respectively. The triple points for the SmC, Cub and Cr-1 phases are estimated as 31.6 +/- 2.0MPa, 147.0 +/- 1.0 degrees C and 11.0 +/- 1.0MPa, 144.0 +/- 1.0 degrees C for BABH(8) and BABH(10), respectively, indicative of the upper limit of pressure for the formation of the cubic phase. The thermodynamic analysis using the Clausius-Clapeyron equation suggests strongly that the Cub-SmC transition with negative slope (dT/dP) accompanies with negative volume of transition. BABH(11) and BABH(12) show the Cr-2-intermediate-temperature crystal (Cr-3)-Cr-1-Cub-I transition sequence at pressures below 10-12 and 16-17MPa, respectively. When higher pressure is applied, the SmC phase with schlieren texture is induced between the isotropic liquid and cubic phases. A biphasic sea-island texture consisting of the SmC and the cubic phases can be seen on heating in the wide pressure region up to 140MPa. These observations exhibit the destabilization of the cubic phase with increasing pressure.