Field-oriented Y1Ba2Cu3Oy samples with various values of the transport critical current density, J(c), have been prepared with various heat treatments. The J(c) increased rapidly with an increase in relative sintered density of the oriented samples. The field-oriented samples with higher J(c) had grains of larger sizes and better connections between the neighboring grains than the low J(c) samples. The maximum values of J(c) at a magnetic field of 7 T were 370 A/cm2 at 4.2 K and 24 A/cm2 at 77 K. The hysteresis in the J(c)-H curves at 4.2 K decreased with an increase in J(c) both for an applied field H parallel-to ab plane and for H parallel-to c axis. The critical currents of the samples with higher J(c) were less degraded by aging in the air for 1 year than those of the low J(c) samples. The relation between the field-cooled J(c)-H curves and the zero-field-cooled ones for an oriented sample with low J(c) is qualitatively interpreted by the effect of the intragrain currents on the intergrain fields.