We mapped 21 star-forming regions with the ^12^CO, ^13^CO and C^18^O (1-0) lines using the 13.7-m telescope of Purple Mount Observatory. This mapping survey resolved 53 ^13^CO cores, of which 22 are sourceless. We obtained the physical parameters of these cores. The relation between ^13^CO linewidth and core size and that between column density and core size were analysed. The cores 00211+6549-1 and 22566+5830 were found to have outflows. Systematic VLSR shifts were detected in nine regions: 00211+6549, 00232+6437, 05168+3634, 19199+1358, 20160+3911, 22566+5830, 23042+6000, S146 and S270. Signatures of infall and cloud collision were found in regions 18507+0121 and 19199+1358, respectively. We studied the mass function of these ^13^CO cores. The core masses range from 3.40 to 4.64x10^4^M_{sun}_, and the core mass function is a power-law distribution of index -0.82+/-0.04.