We have performed ab initio density functional theory calculations with the generalized gradient approximation to investigate CO oxidation on Ru(0001). Several reaction pathways and transition states are identified. A much higher reaction barrier compared to that on Pt(111) is determined, confirming that the Ru is very inactive for CO oxidation under UHV conditions. The origin of the reaction barrier was analyzed. It is found that in the transition state the chemisorbed O atom sits in an unfavorable bonding site and a significant competition for bonding with the same substrate atoms occurs between the CO and the chemisorbed O, resulting in the high barrier. Ab initio molecular dynamics calculations show that the activation of the chemisorbed O atom from the initial hcp hollow site (the most stable site) to the bridge site is the crucial step for the reaction. The CO oxidation on Ru(0001) via the Eley-Rideal mechanism has also been investigated. A comparison with previous theoretical work has been made.