The food bank, which has been running since 2010, has seen a rise in the number of families requesting emergency food parcels from them over the past year.
Many of the residents needing support have been referred for help by Citizens Advice and the Job Centre.
The news comes as recent figures show 81 households with children were threatened with homelessness in Boston last year, compared to 28 the previous year.
Bob Taylor, Food Bank Manager, said: "We are getting 14 to 21 families come in every week because they can't cope with their costs.
"Many people we see through our doors not only are struggling with the cost of food but also have trouble with rent arrears, debt, unexpected bills or issues with benefits and universal credit, so we now have internal channels in which we can point them to for help and advice.
"Today’s cost-of-living crisis means people are choosing between keeping the lights on and putting food on the table so even simple things like budgeting skills, the warm home discount, any grant opportunities available, can really help.”
Boston Food Bank is part of the nationwide Trussell Trust and led by the Parish of Boston.
Chair, Revd Sally Clifton, who helps with logistics and collections, said: "The food bank is open on Tuesdays and Thursdays for two hours each day and we have seen a footfall increased from eight to 12 per session and we expect it to increase even further in the coming months.
"In the last couple of months, we have depleted our supplies and haven't been able to obtain all required stock. Generally food is the biggest issue at the moment.”
Bob added: “The Food Bank functions on six volunteers and myself as manager. With funding from Trussell Trust last year we have been able to fund a Citizens Advice representative to be present at the Food Bank sessions and this has proven to be invaluable.”
Boston Food Bank has seen donations over the years from local residents, businesses and community groups including BTAC, local council Household Support Funds, Tesco, Asda, The Co-op, Lidl and local allotment groups.
It is now appealing for extra donations of fresh fruit and vegetables, fish, biscuits, tea, coffee, juice, long life milk, shampoo, shower gel, toothpaste, deodorant, and shaving items.
Donated items can be dropped off at Blenkin Memorial Hall, in Wormgate, on Tuesdays and Thursdays, from 12-2pm.
• Department for Levelling Up, Housing and Communities figures show 81 households with children were owed a prevention duty in Boston in 2021-22 – up from 28 the year before.
This means the household has been threatened with homelessness and is eligible for local council support.
A further 17 households were owed a relief duty in the year to March, meaning they are already homeless and Boston council must take reasonable steps to help the applicant to secure accommodation for at least six months.