We present CO observations toward three large supernova remnants (SNRs) in the third Galactic quadrant using the Purple Mountain Observatory Delingha 13.7m radio telescope. The observations are part of the high-resolution CO survey of the Galactic plane between Galactic longitudes l=-10deg to 250deg and latitudes b=-5deg to 5d. CO emission was detected toward the three SNRs: G205.5+0.5 (Monoceros Nebula), G206.9+2.3 (PKS 0646+06), and G213.0-0.6. Both of SNRs G205.5+0.5 and G213.0-0.6 exhibit the morphological agreement (or spatial correspondences) between the remnant and the surrounding molecular clouds (MCs), as well as kinematic signatures of shock perturbation in the molecular gas. We confirm that the two SNRs are physically associated with their ambient MCs and the shock of SNRs is interacting with the dense, clumpy molecular gas. SNR G206.9+2.3, which is close to the northeastern edge of the Monoceros Nebula, displays the spatial coincidence with molecular partial shell structures at VLSR~15km/s. While no significant line broadening has been detected within or near the remnant, the strong morphological correspondence between the SNR and the molecular cavity implies that SNR G206.9+2.3 is probably associated with these CO gas and is evolving in the low-density environment. The physical features of individual SNRs, together with the relationship between SNRs and their nearby objects, are also discussed. ; Comment: 29 pages, 20 figures. Accepted for publication in the ApJ