The company, which has its main headquarters in Bridge of Allan plus further operations in Annan, Glasgow and East Kilbride, saw turnover rise 6.5% from £218.4 million to £232.6m.
That came mainly from UK sales, which went up from £163.5m to £185.8m. European turnover dipped from almost £54.9m to £46.8m.
Tony Kirkbright, finance director, said the UK growth came from new product developments and strategic expansion with certain customers.
He said: "If you look at the previous year, a lot of work had been done to negotiate price increases with customers and we started to see the benefit of that in the 2013 financial year, particularly in the second half."
The dip in European sales was put down to currency exchange rates and a general weakening of demand related to the economic woes of countries in the south of the continent.
Annual accounts filed at Companies House for JW Galloway show pre-tax profits grew from £1.13m to more than £4.3m in the 53 weeks to March 3.
The family-owned business, headed by chairman Ian Galloway and his son Robert, who is managing director, includes the Scotbeef and Vivers Scotlamb brands among its subsidiaries.
Writing in the accounts, the directors said: "Livestock prices continued to rise throughout the year, driven by availability and feed costs. Continuing economic pressures in the UK retail market made it difficult to pass on all of these increases, however increased volumes improved operational efficiency."
The directors said operating margins had improved from 0.5% to 1.9% and they continued to look at business development opportunities and making the company, which supplies the likes of Sainsbury's and Marks & Spencer, as environmentally "effective" as possible.
They added: "The group continues to invest heavily in product development, with the aim of increasing its and its customers' market share.
"The export market has offered business development opportunities and the group is looking to exploit these further over the forthcoming year, despite the strengthening Euro."
Net debt was cut from £6.3m at February 26, 2012, to £5.89m by March 3 last year.
Average staff numbers dropped from 774 to 749 through a reduction in slaughter, manufacturing and processing workers.
Even though staff numbers dipped payroll costs were up from £17.7m to £18.5m.
Directors' emoluments fell from £548,000 to £502,000 with the highest paid seeing their remuneration drop from £203,000 to £176,000.
Mr Kirkbright said trading in the current financial year had been strong but cost increases across the industry, partly as a knock on effect from the horse meat scandal, were having an impact.
He said: "Cattle prices have gone up between 13% and 15% and that is a lot to pass on [to customers].
"The forecast is for top line growth in the current trading year but given the cost increases I would be surprised if it manifested in the bottom line."