We analyze CO and H2 absorption lines of the foreground molecular cloud in the Carina nebula. We use HST-STIS (Hubble Space Telescope - Space Telescope Imaging Spectrograph) & IUE (International Ultraviolet Explorer) INES data to analyze the A-X (v=0→2) absorption band of CO for several hot stars toward the Carina nebula, while 9 stars of them have FUSE (Far Ultraviolet Spectroscopic Explorer) spectra to analyze the (v=0→4) vibrational band in the Lyman series of H2. The column densities of CO and H2 varies in the vicinity of N(CO) ~ 1013
−2 and N(H2) ~ 1019
−2, respectively. The resultant CO-to-H2 abundance ratio is about 10−6. We investigate the variation of the abundance ratio according to the relative position of the target stars to morphology the molecular cloud in the Carina nebula.