We prepared single-crystal samples of hexagonal R2Ni12P7 (R = Sm, Gd-Lu) using a Sn-flux method, and measured their magnetization, resistivity, and specific heat. The antiferromagnetic order in Gd2Ni12P7 and Ho2Ni12P7, the ferromagnetic order in Dy2Ni12P7 and Er2Ni12P7, and the ferromagnetic-like order in Sm2Ni12P7, Tb2Ni12P7, and Tm2Ni12P7 were evidenced by the results of the measurements. In contrast, we found that Yb2Ni12P7 is in a heavy fermion state at low-temperature region. Hump-type anomalies in specific heat were observed below the magnetic transition temperature in R2Ni12P7 (R = Gd, Tb, and Dy), indicating the Zeeman splitting of the J-multiplet of the R3+ ion in the ordered state.