The small-sized ConO (n = 1-5) clusters with different spin states have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, and magnetic properties are discussed. Equilibrium geometries and the relative stabilities in terms of the calculated fragmentation energies are discussed, manifesting that the remarkable stable small-sized cluster corresponds to the Co2O isomer, and that the O atom prefers the surface-capped pattern on Co-n (n > 2) clusters and bonds with three Co atoms simultaneously. Furthermore, the calculated averaged atomic magnetic moments of ConO (n = 1-5) clusters exhibit that the septet Co2O structure has the biggest averaged atomic magnetic moment of 2.0 mu(B)/atom, it is interesting that the oxygen capped Co-n (n = 1-5) clusters retain the magnetic properties of bare transition metal (TM) Co-n clusters. In addition, the distribution of electron density of the HOMO states for the most stable ConO clusters mainly localizes around Co-n atoms while the distribution around O atom is very low, and their shapes of the HOMO and bonding properties between bare Co-n clusters and ConO clusters are obviously different. The calculated electron affinities and experimental results (J. Phys. Chem. A 2002, 106, 4891) show that the incoming oxygen atom causes a minor influence on the electronic properties of Co, clusters. Comparisons of the calculated ionization potentials (lPs) for CoO and Co2O clusters with available experimental measurements are made.