Partial Re (rare earth elements: Lu, Yb and Dy) substituted YBaCuO (123) superconductors synthesized by solid-state reaction (SSR) procedure have been investigated via x-ray diffraction, scanning electron microscopy, a.c. magnetic susceptibility, and d.c. magnetization, and calculations. The measurements of a.c. magnetic susceptibility have been carried out at constant a.c. field amplitude and constant frequency for the samples studied. The temperature dependence of intergranular critical current density (J(cm)) has been estimated from the a.c. magnetic susceptibility data. The d.c. magnetization measurements were performed at the temperatures of 5 K, 20 K, and 77 K separately. The variation of critical current density (J(c)) with magnetic field (mu H-0) has been evaluated from the d.c. magnetization data by using upper and lower branch of the major hysteresis curve. Lu substituted Y0.5Lu0.5BCO (123) sample shows higher critical current density than Yb and Dy substituted samples at low-temperature (lower than 77 K) regions.