The critical current densityJc(B,T) of epitaxial YBa2Cu3O7−x(YBCO) thin films on LaAlO3was measured under different applied magnetic fields (0–7 T) with the temperature ranging from 65 to 79 K. At 65 K, the zero‐field critical current density of the best film was 5.8×106A/cm2; even at magnetic fields up to 7 T,Jccould reach as high as 1×106A/cm2. Strong anisotropy was observed at 79 K. The anisotropy behavior diminished with the decrease of temperature. Experimental results showed thatJcwas proportional to (Tc−T)3/2; this was in accordance with the theoretical explanation by the Josephson junction model for granular superconductors.