We present a detailed study of the field (B) - temperature (T) phase diagram of the heavy-fermion antiferromagnet Ce7Ni3 that crystallizes in the hexagonal Th7Fe3-type structure with three nonequivalent Ce sites (CeI, CeII, and CeIII). This compound undergoes two magnetic transitions at TN1 = 1.9 K and TN2 0.7 K in zero field. Below TN1, an incommensurate spin density wave (SDW) develops, and below TN2 a commensurate SDW appears independently. By applying fields along the c axis, both TN1 and TN2, are suppressed and vanish at 0.3 T. For B∥c > 0.7 T, however, another magnetic phase appears below 0.5 K, which was found by magnetoresistance, specific heat, and magnetization measurements. The separation of the field induced phase from the SDW phase is attributed to large spin fluctuations of CeIII, which originate from a geometrical frustration in the quasiregular tetrahedron made of CeI and CeIII.