People can also get free and impartial advice on how to improve the energy efficiency of their homes.
Talking at the launch of the scheme, the company's mortgage head John Barker said: "As houses are one of the largest sources of carbon dioxide emissions in the UK, all mortgages from the Co-operative Bank currently include an annual donation to Climate Care, which enables one fifth of the average home's annual carbon dioxide emissions to be offset.
"However, this new product now goes one step further by actually helping to encourage customers to further reduce their CO2 emissions."
Energy provider Scottish and Southern Energy recently launched a new tariff which also rewards their customers for reducing their energy use over a year.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.