Drax, which generates 5% of the UK's power, has said it plans to capture more carbon than it produces by 2030.
The firm's power plant in North Yorkshire is already largely powered by renewable fuel such as wood pellets.
The trees that the pellets come from absorb carbon, which is then collected when they are burned to generate power.
But, biomass has proved controversial with some environmental campaigners who are concerned about the amount of carbon dioxide created by burning it.
Drax, which is the UK's largest power station, used to run exclusively on coal, but it has converted four of its six units to burn wood as the country seeks to end its dependence on finite fossil fuels.
Drax said that it hopes to install carbon capture technology at two of its biomass units by the end of the next decade.
It said that would remove 8 million tonnes of carbon dioxide from the atmosphere each year. It would be able to double that if the system is applied to all four of its biomass units.
Drax also plans to close the two remaining coal generating units at its North Yorkshire plant by 2025, although the company did not say how that would affect power output.
At present, a pilot project at the site captures a tonne of carbon each day.
But that is only a fraction of the amount that the UK will need to take out of the atmosphere if the country is to achieve its goal of eliminating the greenhouse gasses it produces by 2050.
And a Chatham House report from 2017 suggests burning wood is not carbon-neutral, as young trees planted as replacements absorb and store less carbon than the ones that have been burned.
Prof Nilay Shah, head of the chemical engineering department at Imperial College London, told the BBC the country would need to produce up to 150 million tonnes of "negative emissions" to meet its net zero target.
The power company's chief executive, Will Gardiner, said: "The UK Government is working on a policy and investment framework to encourage negative emissions technologies, which will enable the UK to be home to the world's first carbon negative company.
"This is not just critical to beating the climate crisis, but also to enabling a just transition, protecting jobs and creating new opportunities for clean growth - delivering for the economy as well as for the environment."