In this study, we measured the temperature-dependent magnetic susceptibility [chi(T)], ac magnetic susceptibility [chi(ac)(T)], specific heat [C-p(T)], and high-field magnetization [M(H)] of a newly synthesized single-crystalline material, Co3TeO6. Two transitions were observed in chi(T) and C-p(T) curves at values of T-N1 and T-N2 of approximately 26 and 18 K (H = 0), respectively. The high-field M(H) curves exhibited strong magnetic anisotropy and several field-induced transitions, suggesting that the magnetic ground state was complicated. Large spin-lattice coupling was evident by the large hysteresis in the M(H) curves and through analysis of the specific heat data. We propose herein an H-T phase diagram that is consistent with our experimental findings.