The invention provides a catalyst comprising a transition metal compound which has a nitrogen-containing tridentate ligand and of which the transition metal is of Groups 8 to 10 of the Periodic Table, and an organoaluminium compound, the catalyst of the invention has high activity. In the method of using the catalyst for producing polyolefins, of which the advantages are that the catalysts do not require methylaluminoxane which is expensive and difficult to handle, and of which storage stability is poor, and is extremely dangerous. The invention realizes efficient production of polyolefins (especially polyethylene) on an industrial scale.