The manganese tellurate Li2MnTeO6 consists of trigonal spin lattices made up of Mn4+ (d3, S = 3/2) ions. The magnetic properties of this compound were characterized by several experimental techniques, which include magnetic susceptibility, specific-heat, dielectric permittivity, electron-spin-resonance, nuclear magnetic resonance (NMR), and neutron powder-diffraction measurements, and by density functional theory calculations. The magnetic susceptibility χ(T ) demonstrates very unusual behavior. It is described by the Curie-Weiss law at high temperature with Curie-Weiss temperature of  = −74K and exhibits no obvious anomaly indicative of a long-range magnetic ordering at low magnetic fields. At high magnetic fields, however, the character of χ(T ) changes showing a maximum at about 9 K. That this maximum of χ(T ) reflects the onset of an antiferromagnetic order was confirmed by specific-heat measurements, which exhibit a clear λ-type anomaly at TN ≈ 8.5K even at zero magnetic field, and by 7Li NMR and dielectric permittivity measurements. The magnetic structure of Li2MnTeO6, determined by neutron powder-diffraction measurements at 1.6 K, is described by the 120◦ noncollinear spin structure with the propagation vector k = (1/3, 1/3, 0). Consistent with this finding, the spin-exchange interactions evaluated for Li2MnTeO6 by density functional calculations are dominated by the nearest-neighbor antiferromagnetic exchange within each triangular spin lattice. This spin lattice is strongly spin frustrated with f = ||/TN ≈ 8 and exhibits a two-dimensional magnetic character in a broad temperature range above TN.