We report nanostructure electrodes with $TiO_2$ as a core and carbon as a shell ($TiO_2$@C) for oxygen reduction in alkaline solution. The structure of core-shell electrodes is characterized by transmission electron microscopy, Raman spectroscopy, X-ray diffraction method, and X-ray photoelectron microscopy. The electrochemical properties of the $TiO_2$@C electrodes are characterized using a potentiostat and compared with those of carbon supported Pt catalyst. In particular, the core-shell electrode with dominant pyridinic-N component exhibits an imporved electrocatalytic activity for oxygen reduction reaction in alkaline solution.