Congruent and nearly stoichiometric LiNbO3 single crystals doped with Co2+ ions have been investigated by the electron paramagnetic resonance technique. The spin-Hamiltonian parameters, g|| = 2.671(2), g = 5.052(2), A|| = 40(2) × 10-4 cm-1, and A = 154(1) × 10-4 cm-1, are obtained without including the nuclear Zeeman and quadrupole interactions. The factor, k, of reduction due to the covalency is estimated as 0.92 k1 using the above g-values. On the basis of the temperature dependence of the linewidth, the spin-lattice relaxation and the spin-spin relaxation mechanisms are investigated. The former is a sum of a weak direct process with a phonon bottleneck (~T2.4) and an Orbach process with ~156 cm-1 (or 225 K), and the latter is a sum of a typical temperature-independent process and an anomalous process with a temperature dependence T-3.6. This anomaly is considered as a shortening of T2 due to the increase of the correlation length of the spin-spin interaction as the temperature decreases. The integrated signal intensity also showing an anomaly is a consequence of the linewidth anomaly.