Using the PMO-13.7 m millimeter telescope at Delingha in China, we have conducted a large-scale simultaneous survey of (CO)-C-12, (CO)-C-13, and (CO)-O-18 J = 1 - 0 emission toward the Rosette molecular cloud (RMC) region with a sky coverage of 3 degrees.5 x 2 degrees.5. The majority of the emission in the region comes from the RMC complex, with velocities lying in the range from -2 to 20.5 km s(-1). Beyond this velocity range, 73 molecular clumps are identified with kinematic distances from 2.4 to 11 kpc. Based on the spatial and velocity distribution, nine individual clouds, C1-C9, have been identified for the RMC complex. It appears that the C3 cloud is different from other clouds in the RMC complex in view of its characteristic velocity, excitation temperature, and velocity dispersion. Most of the young stellar clusters in the region are located in positions of both high column density and high excitation temperature. Seven new molecular filaments are discovered in the RMC complex. Evidence for cloud-cloud collision is found in the region of young stellar clusters REFL9 and PouF, showing that these young stellar clusters probably result from a cloud-cloud collision. The abundance ratios of (CO)-C-13 to (CO)-O-18 in the region have a mean value of 13.7, which is 2.5 times larger than the solar system value, showing that UV photons from the nearby OB clusters have a strong influence on the chemistry of clouds in the RMC complex.