First principles calculations are performed to study the geometric structures and the nitrogen adsorption properties of BaO adlayer on Ru(0001) surface. It is suggested that BaO adlayer is more stable on Ru(0001) surface at low coverage. A configuration is observed in surface phase at low coverage. In this structure oxygen is adsorbed on the hcp site of one p(1 1) cell, and barium is adsorbed close to the top site of the same p(1 1) cell. Bond length of oxygen and ruthenium is calculated to be 0.209 nm, longer than the EXAFS experimental value about 0.018 nm. Nitrogen prefers to be adsorbed on the sites close to barium. Nitrogen adsorption energies at those sites are calculated to be in a range from 0.70 to 0.87 eV, which are bigger than those at the sites close to oxygen. Adsorption sites near barium atoms have more activities to weaken nitrogen. The lowest N-N stretching vibrational frequency on the sites is about 1946 cm-1, less than the highest frequency on sites around oxygen (about 130 cm- 1). Bond strengths of nitrogen on Ru(0001) /BaO surface are between those on clean Ru(0001) and Ru(0001) /Ba surface. The adsorption properties of sites around BaO layer are determined by chemical characteristic of barium and oxygen. Electron transfer from barium to ruthenium enhances the hybridization between ruthenium and nitrogen by reducing and increasing the occupation of * and * orbitals respectively.