We present high-resolution simultaneous observations of the edge-on galaxy NGC 891 in 12CO and 13CO emissions. The molecular thin-disk component within 10.7 kpc from the galactic center was completely covered. This data set with accurate relative calibrations of intensity scale and pointing is analyzed to examine radial variation in the physical properties of the molecular gas. The total 13CO/12CO luminosity ratio is 1/6.6. A low 13CO/12CO intensity ratio of 1/(15.4 +/- 6.0) is observed in the nuclear disk of about 550 pc in radius. There exists a systematic gradient of the 13CO/12CO intensity ratio in the main galactic disk as a function of galactocentric distance: the 13CO/12CO intensity ratio exhibits a notable peak of ~=1/4.5 near 4 kpc, and decreases systematically outward down to <~1/10 at 10 kpc. The observational results are analyzed on the basis of a CO excitation analysis. The low 13CO/12CO intensity ratio in the nuclear disk may be attributed to a predominance of warm molecular gas (>~40 K) of moderate gas density (~103 cm-3), while the systematic gradient of the 13CO/12CO intensity ratio in the main disk can be interpreted in terms of radial decrease in the dense molecular gas fraction. Since interstellar gas in the inner part of the galaxy is mostly molecular, this variation will be ascribed to compression of molecular gas with its strength dependent on galactocentric distance rather than dissociation of low-density molecular gas by UV photons from young stars in the inner part of the galaxy.