Charity the Trussell Trust says 51,474 adults and 22,258 children have used its service since April – 2,000 more than at this time last year.
It is estimated that by next April, the figure could rise above 90,000 people.
More than 700 tonnes of donated food has been received by the trust, with more than 540 tonnes distributed.
Figures show Dundee has had the highest number of adults using food banks in the past year, at 3,750, while Glasgow South East has the highest number of children, at 1,975. South Skye and Lochalsh had the lowest number, with just 32 adults and 19 children receiving a three-day supply of groceries.
Ewan Gurr, the trust’s network manager in Scotland, said low pay and welfare reform were the main factors driving the growing demand for food parcels.
He also said the charity was seeing more middle-class people using the service.
Mr Gurr said: “There are four recurring factors stated by the people using our service in Scotland. The first is the rising cost of food and fuel, the second is low income and insecure employment, the third is minimum employment opportunities for those looking to get back into work, and the fourth is welfare reform.
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“Welfare reform and low pay are the two main drivers.”
Asked whether he felt the increased awareness of food banks as a service could explain the rise in users, he said: “There is no empirical evidence to suggest that the increase in demand is supply-led.
“I ran a food bank in Dundee for seven years until 2012 and that year the number of users doubled without any increased advertising or marketing.
“The service had always been there; all that had changed was that effects of welfare reform began to bite.”
The trust – which has 48 centres in Scotland, against just one operating in partnership with the trust in 2011 – opened its doors on Christmas Day and served a festive dinner to hundreds of people.
Scottish Labour social justice spokesman Ken Macintosh MSP said: “These are deeply worrying and depressing figures. I think most families would like to look forward to a new year with a sense of optimism and opportunity, but I fear for many the problem is only getting worse.
“The work of the Trussell Trust is fantastic, but more needs to be done by both the Westminster and Scottish governments to tackle the shameful problem.”
A Scottish Government spokeswoman said: “It is unacceptable that anyone should experience food poverty in a country as wealthy as Scotland. We know from the Trussell Trust that welfare and benefit changes are having a significant impact on the most vulnerable in Scotland.
“Efforts to tackle economic inequalities in Scotland are being made in the face of a welfare reform programme that is estimated to reduce benefit expenditure by around £6 billion in Scotland in the six years to 2015-16.”
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