We investigated the critical current densities (J cb ) at grain boundaries (GB) of bicrystalline Nd 1 Ba 2 Cu 3 O 7−δ films. We observed that these sharply dropped as the applied fields were increased from zero to ∼1 Oe (H JA ) and then showed relatively small field dependences above H JA . These contrasting field dependences of J cb below and above H JA clearly indicated crossover phenomena in the vortex states. Our experimental results were consistent with a theoretical model, which was based on the concept that the energy difference between Josephson (J-) vortices and Abrikosov (A-) vortices caused the generation of only J-vortices initially. This might result in an initial sharp increase of J-vortex densities at GB, as the field is increased from zero to H JA . As the field is increased further, some J-vortices penetrate from GB to intra-grain regions and become A-vortices, which might change the field dependences of J cb .