The Greens want a threefold increase in the levy on the nation's big banks in a move it says would raise almost $10 billion over the next three years and help smaller institutions woo new customers.

In a policy that the independent Parliamentary Budget Office assumes would be mostly paid for by customers and shareholders, the Greens are demanding the levy be increased to 0.05 per cent from its current level of 0.015 per cent.

The levy, which is tax deductible for the banks, is expected to raise $1.65 billion this financial year.

The Greens want to triple the bank levy in a plan that would raise $40 billion over the next decade Credit:Ian Waldie

Under the Greens proposal, it would raise an additional $2.8 billion in its first year of operation before increasing to $3.4 billion. Over a decade, the higher levy would raise an extra $40.2 billion, according to PBO estimates.