Computational studies have been carried out on the LiNi1-xCoxO2 compounds based on density-functional theory. Quantum-mechanical calculations are performed using a total-energy pseudopotential code. Density of states and partial density of states are calculated with the considering the spin state of Ni and Co. Electronic structure calculations suggest that the exchange splitting is controlled by Co content. As the Co content increased, the exchange splitting decreased. Electronic structure calculations show that the crystal field splitting is controlled by the second content. With Co contents increasing, the crystal field splitting decreased for LiNi1-xCoxO2 with x=0, 1/3 and 2/3. The study also shows that the interaction of Ni ion with surrounding O ions and Li ions will be changed and prevents Li ions from leaving LiNiO2 with the increasing substitution Co for Ni in LiNiO2.