The bank has teamed up with Christian Aid for the campaign, which aims to gain a million signatures on a petition to be submitted to the UK government and calling for an overhaul of trade agreements.
The charity and the bank say current free trade agreements constrain developing countries, which should be given more power over world trade policy making.
The campaign has been developed by agency The Farm and features posters with a pair of hands locked together with a padlock with the work "free trade" written across it.
The poster also features the slogan, "There's nothing free about free trade", and aims to drive traffic to a where visitors can pledge their support to the campaign.
Simon Williams, Co-operative Bank corporate affairs director, said: "We have a strong reputation for campaigning on behalf of our customers and with this press ad we want to continue to raise awareness among the UK public of the huge need for trade justice for the world's poorest countries."
This is the latest push under the bank's "customers who care" corporate social responsibility banner.
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