Abstract : We report on the gamma-ray observations of giant molecular clouds Orion A and B with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. The gamma-ray emission in the energy band between ∼100 MeV and ∼100 GeV is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the Galactic cosmic rays (CRs) and interstellar gas. The gamma-ray production cross-section for the nuclear interaction is known to ∼10% precision which makes the LAT a powerful tool to measure the gas mass column density distribution of molecular clouds for a known CR intensity. We present here such distributions for Orion A and B, and correlate them with those of the velocity-integrated CO intensity (WCO) at a 1◦ × 1◦ pixel level. The correlation is found to be linear over a WCO range of ∼10-fold when divided in three regions, suggesting penetration of nuclear CRs to most of the cloud volumes. The WCO-to-mass conversion factor, XCO, is found to be ∼2.3 × 1020 cm−2 (K km s−1)−1 for the high-longitude part of Orion A (l > 212◦), ∼1.7 times higher than ∼1.3 × 1020 found for the rest of Orion A and B. We interpret the apparent high XCO in the high-longitude region of Orion A in the light of recent works proposing a nonlinear relation between H2 and CO densities in the diffuse molecular gas. WCO decreases faster than the H2 column density in the region making the gas "darker" to WCO.