This article reports first-principles band structure calculations for RMn6Sn6 (R=Tb, Dy). The calculation uses the linear muffin-tin orbitals (LMTO) method in the atomic-sphere-approximation (ASA), and yields results showing that both TbMn6Sn6 and DyMn6Sn6 are ferrimagnetic compounds with antiparallel aligned moments of R and Mn atoms. In this research the 4f states of R atoms are treated as localized states, i.e., the hybridization of 4f states with other valence electrons is neglected. The moments of Mn in both compounds were determined to be 2.43 μB and 2.38 μB, respectively. The considerably small additional moments for Mn from the spin-orbit coupling indicates that the spin-orbital coupling is not dominated for Mn atoms. The total moments of Tb and Dy atoms are 10.28 μB and 11.20 μB. All the calculation findings accorded well with experimental results.