Car finance was up by 27% in May compared with May 2011.
More businesses are investing in fleet vehicles than they were a year ago - whether replacing old fleet cars, or investing in new ones.
Plant and machinery finance, and IT equipment finance also showed very strong growth.
There was also strong growth in the sales finance channel with 27% more finance provided through commercial vehicle sellers, tractor suppliers, computer suite vendors, and other equipment suppliers than in May 2011.
Sales finance accounted for 29% of all asset finance provided to businesses in May.
Geraldine Kilkelly, head of research and chief economist at the Finance & Leasing Association, said: "Asset finance is now very much on an upward curve. At current growth rates, the total asset finance market for deals worth up to £20m will be back to pre-credit crunch levels by 2015.
"High acceptance rates in the asset finance market have meant that lenders are able to help a large number of businesses with their investment needs. New Government schemes have involved some asset finance lenders, helping them to lend even more. We are now asking that the new Funding for Lending scheme be opened to all lessors - including those who have not qualified for previous Government assistance schemes."
