A newly released draft policy from the bank said rapid and drastic action was needed to fight climate change and meet the objectives of the Paris Agreement.
The world is currently not on target to meet the commitment in the Paris Agreement to limit the global temperature increase to 1.5C.
The EU is still largely dependent on fossil fuels for transport, industry and heating, and many member states continue to rely on them for power generation.
This is despite the fact that in the last five years alone, the EIB has lent about €12 to 14bn in the energy sector every year, largely towards energy efficiency, renewable energy and energy grids.
But under the draft policy, the bank would stop its support for oil and gas production, infrastructure primarily dedicated to natural gas and power generation and heat based on fossil fuels.
Alex Doukas, lead analyst with campaign group Oil Change International, said: “The European Investment Bank’s proposal to end financing for fossil fuels by the end of 2020 is a massive step forward on climate leadership.
“With this move, the world’s largest multilateral lender is now poised to leave oil, gas, and coal in the past.
“The European Union member states who control the bank must now stand behind the EIB’s game-changing climate leadership by swiftly approving this new policy, and other financial institutions should quickly follow suit and stop funding fossils.”
As well as axing support for fossil fuels, the EIB plans to step up its support for innovative low-carbon technology “from the earliest stage in the research lab”.
It will also aim to support member states’ own energy and climate plans, and help groups or regions with a more challenging transition path to green energy.
EIB vice president Andrew McDowell said the policy would help the bank’s ambition “to position itself as the EU’s climate bank”.
He said: “The main proposals are clear. We want to increase our support for the energy transition in Europe, the decarbonisation of the European economy.”
The policy will be discussed by the EIB board of directors on 10 September and is expected to be adopted.