Deputy leader Amelia Womack said the proposed increase would be "life changing" for families.
The Greens are also pledging to reverse cuts to welfare as part of efforts to "protect the most vulnerable".
The pledges, announced as the party unveiled its campaign bus in Bristol, would be paid for by increasing tax for the wealthiest, Ms Womack said.
This election issue includes access to benefits (apart from pensions), poverty and inequality.
Policy guide: Where the parties stand
Child benefit is a tax-free payment aimed at helping parents cope with the cost of bringing up children.
Currently, one parent can claim £20.50 a week for an eldest or only child and £13.55 a week for each of their other children.
The payments apply to all children aged under 16 and in some cases until they are 20 years old.
"We believe in doing more, much more, to redistribute income within our society," Ms Womack said.
"That's why we're being honest about the fact that we'd increase tax for the richest in society - and it's why we're able to pledge that we'd double child benefit to £40 a week.
"For the 29% of children here in Bristol West who live in poverty, this increase will be life changing."
The party also wants to retain the Independent Living Fund that helps disabled people to live and work in the community, and which is due to close on 30 June 2015.
"We won't stand by while this lifeline is cut away," said Ms Womack, estimating that the policy would cost £300m.
The deputy leader said the Greens would always stand for an economy that "works for the many", adding: "That means our MPs will never blame the most vulnerable for the mistakes of those at the top."
Subscribe to the BBC Election 2015 newsletter to get a round-up of the day's campaign news sent to your inbox every weekday afternoon.
Child benefit would double to £40 a week under plans set out by the Green Party in England and Wales.