Melt grown samples of Y_1.2Ba_1.8Cu_2.4O_x have been prepared and studied for their current carrying capacity. The composition was chosen to include Y₂BaCuO₅ (211) particles in the YBa₂Cu₃O_x (123) phase. The critical current density (J_c) of these samples was studied as a function of magnetic field using magnetization technique. The micrographic investigation shows well aligned grains in this material. The magnetic hysteresis measurements were done using a MPMS SQUID magnetometer up to the fields of 5.5 T. TheJ_c was estimated from the remanent magnetization using Bean model. Isothermal magnetization hysteresis loops at low fields reveal the presence of only one kind of hysteresis loops (corresponding to intragrain magnetizations). This is a valid proof that the weak links are greatly eliminated in these samples prepared by MG process. TheJ_c behaviour as a function of magnetic field has two components, a rapidly decaying exponential function of field and the other component that predominates at higher fields. This could be explained if we assume that the sample contains two phases of superconductors, one having a lowH_c2 becoming normal at fairly medium fields of the order of a few kilogauss will act as pinning centres for the other phase having higherH_c2 and hence higherJ_c at high fields.