The present invention provides a hydrogenation catalyst, which can produce an olefin polymer having a higher molecular weight, and a process for producing an olefin polymer having a higher molecular weight, by controlling hydrogen concentration in a polymerization reaction system efficiently in polymerizing an olefin in the presence of hydrogen. There is provided a hydrogenation catalyst formed by contacting the undermentioned component (A), the undermentioned component (B), and the undermentioned component (C). There is further provided a process for producing an olefin polymer characterized by polymerizing an olefin in the presence of hydrogen, the undermentioned component (A), the undermentioned component (B), and the undermentioned component (D). Component (A): a titanocene compound; Component (B): a silicon compound represented by the undermentioned general formula [1]: Si(OR1)4 [1]; Component (C): an alkyl metal compound; Component (D): a catalyst for olefin polymerization.