We investigated the critical current densities (J(cb)) at grain boundaries (GB) of bicrystalline Nd1Ba2Cu3O7-delta films. We observed that these sharply dropped as the applied fields were increased from zero to similar to1 Oe (H-JA) and then showed relatively small field dependences above H-JA. These contrasting field dependences of Jcb 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).