Process for producing olefin polymer

The purpose of the present invention is provite a process for producing an olefin polymer, which can produce an olefin polymer having a higher molecular weight even in the presence of hydrogen and can obtain an olefin polymer having good powder characteristics by lowering hydrogen concentration efficiently in polymerizing an olefin in the presence of hydrogen by use of a gas phase reaction vessel. There is provided a process for producing an olefin polymer comprising the steps of: using a gas phase reaction vessel; polymerizing an olefin by use of a catalyst for olefin polymerization in the presence of hydrogen; adding a hydrogenation catalyst into the gas phase reaction vessel; and adding a polymerization activity depressant.