The Rt Rev Paul Butler, has put his name to the End Hunger UK (EHUK) petition, calling on the Government to "fix" Universal Credit to prevent more people going hungry.
He has also urged churches and churchgoers to do the same.
The campaign also calls for improvements to the design of Universal Credit and a long- term commitment to ensure the benefit provides people with an adequate income to afford good food on a regular basis.
Bishop Paul has written to all the Bishops in the Church of England encouraging them to join him in signing the petition.
He said: "We are all well aware of the reality for too many families that making ends meet and providing adequate healthy food for children is very hard.
"This is borne out by many churches in the diocese getting involved in summer holiday clubs that provided food and fun for large numbers of such families during the school holidays.
"I have signed the End Hunger UK petition, calling on the Government to fix Universal Credit to prevent more people going hungry. I am also encouraging parishes and churchgoers across the diocese to do likewise."
He added that while he supports the principle of Universal Credit, the system has many flaws that need to be addressed.
"More and more families have had to turn to food banks following the introduction of Universal Credit, and are reporting unintended delays, lack of digital support, poor administration, and a lack of flexibility in the system. All of these problems can and should be resolved," Bishop Paul said.
In the Diocese of Durham there are five Trussell Trust food banks working out of 44 distribution centres, which last year distributed 33,292 three-day emergency food parcels to people in crisis. There are also at least 24 independent food banks.
"We need urgent action to improve the flexibility and support for people on Universal Credit, and a long-term commitment that the social security system will provide enough income to afford good food on a regular basis.
"Without such action, we can expect to see more and more people turning to food banks and becoming trapped in poverty, as more people are moved on to Universal Credit," he said.
Bishop Paul's letter comes as a report by the Resolution Foundation published on Friday states the "design flaws" in the Universal Credit system need to be resolved this Autumn to avoid further issues and potentially leading people to not applying for the scheme.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.