We analyze CO and H-2 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 H-2 varies in the vicinity of N(CO) similar to 10(13) cm(-2) and N(H-2) similar to 10(19) cm(-2), respectively. The resultant CO-to-H-2 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.