EPR measurements on single crystals of Cu2+molecular ion doped in Thallium Cobalt Sulphate Hexahydrate, Tl2Co(SO4)2. 6H2O have been performed over the temperature range 120–390 K, at X-band (≈9.205 GHz). The orientation dependence EPR spectra reveal that the impurity ions enter at the divalent cobalt site in the lattice, exhibiting two symmetry related equivalent complexes. The principal parameters have been estimated and found to be axially symmetric and dependent on temperature. The Fermi contact term (K) and covalency parameter (α) are evaluated from the principal parameters.