We present here our studies on Zn-doped La 1 . 5 Nd 0 . 5 Ca 1 Ba 2 Cu 5 O z (La-2125), tetragonal superconductor. Eight different compositions of La 1 . 5 Nd 0 . 5 Ca 1 Ba 2 (Cu 1 - x Zn x ) 5 O z (x=0.00-0.04), were studied through X-ray diffraction, SEM, a.c. susceptibility, resistivity, magnetization measurements and iodometric analysis to explore effects of Zn doping on the structural and superconducting properties. The Rietveld analysis of XRD data shows that all the samples form in tetragonal structure (space group P4/mmm). A.c. susceptibility and resistivity measurements showed that, superconducting transition temperature, T c , is suppressed with increasing Zn in the system at the rate of ~6-7 K per atomic percent of Zn. The superconducting transition of these materials is found to be highly dependent on dopant concentration. The critical current density J c (H), determined from magnetization measurements, is found to be ~10 5 -10 6 A/cm 2 at low fields. For x=0.01 and 0.015, J c is higher at all fields and is nearly double than that of the pristine La-2125. The enhancement in J c (H) is ascribed to the effective flux line pinning by nonmagnetic Zn at Cu-O planes in this system. For higher concentrations, due to competition between increase of J c arising from pinning by Zn and decrease of J c arising from pair breaking effect of Zn, a cross over is seen in the J c (H) of doped and pristine samples.