A kind of novel carbene ligand and corresponding novel ruthenium catalyst are provided. The ruthenium catalysts are highly active and selective for ROMP and RCM reactions. The significant electronic effects of different substituted carbene ligands on the catalytic activity and stability of corresponding carbene ruthenium complexes are disclosed. The methods for preparing new ruthenium complexes are disclosed. Moreover, efficient methods for making various functional polymers and quality modified nitrile butadiene rubbers via different metathesis and hydrogenation reactions in the presence of the new ruthenium catalysts are provided.