We report monitoring observations of the T Tauri star EX Lupi during its outburst in 2008 in the CO fundamental band at 4.6-5.0 um. The observations were carried out at the VLT and the Subaru Telescope at six epochs from April to August 2008, covering the plateau of the outburst and the fading phase to a quiescent state. The line flux of CO emission declines with the visual brightness of the star and the continuum flux at 5 um, but composed of two subcomponents that decay with different rates. The narrow line emission (50 km s-1 in FWHM) is near the systemic velocity of EX Lupi. These emission lines appear exclusively in v=1-0. The line widths translate to a characteristic orbiting radius of 0.4 AU. The broad line component (FWZI ~ 150 km s-1) is highly excited upto v<=6. The line flux of the component decreases faster than the narrow line emission. Simple modeling of the line profiles implies that the broad-line emitting gas is orbiting around the star at 0.04-0.4 AU. The excitation state, the decay speed of the line flux, and the line profile, indicate that the broad-line emission component is physically distinct from the narrow-line emission component, and more tightly related to the outburst event.