Magnetic measurements and neutron powder diffraction investigations on the Y3NiSi3-type R3NiSi3 compounds (R=Gd, Tb, Dy) reveal their complex antiferromagnetic ordering. Magnetic measurements on Gd3NiSi3, Tb3NiSi3 and Dy3NiSi3 indicate antiferromagnetic-like transition at temperatures 260 K, 202 K and 140 K, respectively. Also, the Tb3NiSi3 and Dy3NiSi3 compounds show spin-reorientation transition at 132 K and 99 K, respectively. Below the spin-reorientation transition, the isothermal magnetization curves indicate the metamagnetic-like behavior of Tb3NiSi3 and Dy3NiSi3. The magnetocaloric effect of Dy3NiSi3 is calculated in terms of isothermal magnetic entropy change and it reaches a maximum value of -1.2 J/kg K and -1.1 J/kg K for a field change of 50 kOe near 146 K and 92 K, respectively. The neutron diffraction studies of Tb3NiSi3 suggest the magnetic ordering of the Tb2 4j sublattice and no magnetic ordering of the Tb1 2a sublattice. Tb3NiSi3 transforms from the high temperature paramagnetic state to the commensurate high-temperature a- and c-axis antiferromagnet of I′2/m magnetic space group below 250 K. Below 150 K, the high-temperature antiferromagnet transforms into the low-temperature a-, b- and c-axis antiferromagnet of I′i magnetic space group. At 1.5 K, the terbium magnetic moment in Tb2 sublattice and its a-, b- and c-axis components reach the values of MTb2=8.2(1) μB, MaTb2=5.9(1) μB, MbTb2=4.3(2) μB and McTb2=3.7(2) μB, respectively. © 2015 Elsevier B.V. All rights reserved.