Neutron diffraction measurements were performed under high magnetic fields up to 17 T in a multiferroic BiFeO3 single crystal, in which an intermediate magnetic (IM) phase has been found between the cycloid and canted antiferromagnetic phases [S. Kawachi et al., Phys. Rev. Mater. 1, 024408 (2017)]. We clearly found that the incommensurate magnetic peaks, which split perpendicular to the magnetic field in the cycloid phase, rotate by 90 deg to align parallel to the field in the IM phase. The magnetic structure in the IM phase can be best described by an antiferromagnetic cone (AF cone) structure. The transition from the cycloid to AF cone is of first order and the direction of the magnetic wave vector and the easy plane of the cycloidal component are rotated by 90 deg without changing the cycloidal modulation period, whereas the transition from the AF cone to canted antiferromagnetic phase is gradual and the cone angle becomes smaller gradually without changing the modulation period. Interestingly, the cycloidal component as well as the cone angle in the IM phase shows a large hysteresis between the field increasing and decreasing processes. This result, combined with the magnetostriction with a large hysteresis previously reported in the IM phase, suggests a strong magnetoelastic coupling.