In2NiMnO6, a new compound extending the family of double rare-earth perovskites R2NiMnO6 (R = rare earth, Y) to smaller R ions, was prepared using a high-pressure and high-temperature technique (6 GPa and 1600 K). Its crystal structure was investigated by synchrotron X-ray powder diffraction at room temperature: space group P2(1)/n (No. 14, cell choice 2), Z = 2, a = 5.13520(1) angstrom, b = 5.33728(1) angstrom, c = 7.54559(4) angstrom, and beta = 90.1343(1)degrees. A significant degree of ordering of Mn4+ and Ni2+ ions was observed. The dc and ac magnetization and specific heat measurements showed that In2NiMnO6 is an antiferromagnet with a Neel temperature T-N of 26 K. Its antiferromagnetism puts it apart from other members of the R2NiMnO6 family where a ferromagnetic ground state was observed, which is attributed to the superexchange interaction between Mn4+ and Ni2+ ions according to the Kanamori-Goodenough rules. A field-induced phase transition to a ferromagnetic state was observed from 18 kOe at 5 K, indicating that In2NiMnO6 is close to the antiferromagnetic-ferromagnetic transition boundary. First-principles calculations allowed us to explain its antiferromagnetism and the field-induced phase transition and predict the E* type antiferromagnetic ground state.