The invention discloses organic ligand L for synthesizing Cu (I)-based metal organic coordination polymer, and Cu (I)-based metal organic coordination polymers Cu-CPs; the meal organic coordination polymers Cu-CPs are synthesized through the organic ligand L and are of 1D single-stranded structure, having two crystallographically independent Cu metal centers, with one center positioned on 1D strand and connecting imidazole N atoms on two ligands, and with the other positioned outside the 1D strand and having two Br ligands present in the form of [CuBr2]-. There is weak M-M action between the two Cu metal centers. The Cu-CPs are efficient in catalyzing phenylethylene oxide ring-opening reaction, p-bromophenol acetylization and Mannich reaction with no need for heavy metals to engage in catalyst reaction, environmental damage due to heavy metals is reduced, reaction temperature is medium, reaction time is short, little catalyst is used, no other additives are used, and compared with free heavy metal salts, the polymers are available for more than 5 times of reuse.