We report on the growth of a different orientation plane of Ni3TeO6 single crystal by the flux growth method for the first time. X-ray diffraction is used to characterize the single crystal and it crystallizes into the trigonal structure having space group R3 with lattice parameters of a = 5.1087 Å and c = 13.767 Å. The earlier studies reported that the antiferromagnetic (AFM) ordering below T(N) ∼ 52 K confirms to be valid only under high magnetic field. In contrast, the existence of a ferrimagnetic-like ordering due to the antiferromagnetically coupled spins of uncompensated longitudinal staggered moments is revealed from the low field average spin susceptibility data analysis. The spin structure of Ni3TeO6 has been proposed with low magnetic field using single crystal samples. We believe that the Ni ions in the two stacked Ni(I)-Ni(II) and Ni(III)-Te 2D honeycomb ring layers have different spin sizes--the former may have an average moment of S = 3/2 and the latter remains to be S = 1, and the interlayer antiferromagnetic interaction of the ferromagnetically coupled layers leads to the incomplete cancellation below ∼72 K. The ferrimagnetic ordering and the extra paramagnetic spin moment beyond S = 1, observable at low field, can be suppressed with high magnetic field, suggesting the existence of a field-sensitive spin-orbit coupling in Ni3TeO6, that remains to be explored experimentally and theoretically.