In the six months to September, 39,174 people were given three days' emergency food from the network of centres run by the Trussell Trust.
This is a 20% rise on the same period in 2013.
But the Department for Work and Pensions (DWP) said there was "no convincing evidence" linking benefit changes and more use of food banks.
Source: Trussell Trust
CASE STUDY: EBBW VALE
The Blaenau Gwent food bank runs from a church in Ebbw Vale twice a week and was the first to open in Wales in October 2008.
It has helped just over 1,500 people from April to September 2014. This is about 200 fewer people than the same period last year but compares to 900 in April to September 2012.
Martin Abel, food bank manager, said: "All food bank vouchers are numbered and people are allowed up to three so we notice if a pattern is emerging we put them in touch with agencies and find help, whether it's with budgeting or whatever."
Read more - Blaenau Gwent food bank finds goodwill in troubles
In Wales, those helped included more than 13,200 children.
The most common reasons for seeking help are benefit delays, low income and benefit changes.
Oxfam Cymru has blamed a "perfect storm" of "benefit cuts, low wages, sanctions and insecure jobs".
But Works and Pensions Secretary Iain Duncan Smith has said it was "quite wrong" to suggest it was just to do with benefits-related problems.
The DWP has consistently claimed welfare changes are not to blame.
A spokesman added: "The reality is the vast majority of benefits are processed on time, with improvements being made year on year.
"And we continue to spend Â£94bn a year on working age benefits to ensure there is a strong safety net in place."
The number of people using food banks in Wales has continued to rise, according to latest figures for 2014.