The influences of microstructure on the critical current density of a high Tc superconductor YBa2Cu3Ox were discussed on the basis of JC·R measured by the standard four-probe resistive method as well as of JC·M calculated from the magnetization curve at 77K. The microstructure was changed by controlling the sintering temperature and cooling rates. For the specimens sintered at 920°-960°C, JC·R increased and the resistivity decreased as the bulk density increased. A decrease in JC·R for the specimen sintered at 990°C resulted from the incongruent melting of YBa2Cu3Ox. For the specimens sintered at 990° to 1030°C, JC·R increased again by the recrystallization during slow cooling. The intrinsic JC of YBa2Cu3Ox was examined by the Josephson weak links theory from the magnetization data. As a result, the grain size measured with an optical microscope is more suitable compared with the thickness of specimens for the calculation of JC·M. Moreover, the area surrounded by weak links is larger than the grain size of the specimens sintered at 940° to 975°C. The intrinsic JC calculated from the area surrounded by the weak links was almost constant, 2.5×104A·cm-2 at 0.7kOe at the sintering temperature from 960° to 1030°C. JC·R increased by changing the cooling process from 1030°C. This is due to the increase in the area surrounded by the weak links corresponding to the grain growth.