The trust, which runs 420 food banks across the UK, told the BBC that many children risk going hungry over the six-week-long summer holidays as they struggle to cope with the loss of school meals.
It says that the demand for food supplies rose ‘significantly’ during the holidays last year, with 67,506 three-day emergency food supplies provided for children in July and August 2016, up 4,412 from May and June.
The trust says nearly half (47%) of those 67,506 parcels went to primary-school-age children and over a quarter (27%) to children aged four and under.
Speaking to the BBC, Samantha Stapley, operations manager at The Trussell Trust, said: "Over a third of all the food distributed by food banks in our network consistently goes to children, but these new figures show five- to 11-year-olds are more likely than other children to receive a food bank's help.
"This highlights just how close to crisis many families are living - as a nation, we also must address the reasons why families with children are referred to food banks in the first place.
"We welcome the government's decision to maintain free school lunches for children during term time - the next step must be to help families during the holidays.
"Food banks are doing more than ever before, but voluntary organisations alone cannot stop primary school children facing hunger."