However, the group also reported a slight drop in profit amid squeezed profit margins.
The firm, which has been based in Bridge of Allan since 1939, said turnover was up by £16.8 million to £100.5m in the year to March 2017.
It attributed the rise to the full-year impact of the acquisition of the Glenfield Dairy site in Fife that completed in 2016 and an accompanying increase in volumes.
The family-owned farming business also said developing new products remains key to its growth strategy, and in early 2017 it launched Protein 22, a quark-based fruit flavoured snack, which has achieved several Scottish, UK and international listings.
MD Robert Graham said: “We continue to grow our business partnerships with major retailers and now over half the Scottish population buy Graham’s products.
“Going forward, we will constantly innovate to expand our award-winning product range both within the UK and beyond.”
This year also saw the dairy hiring what it says is the UK’s first milk sommelier, while there was continued investment of £1.4m in new plant and machinery.
Additionally, it built a logistics facility depot in Kintore, which it said boosted its commitment to customers and suppliers in Aberdeenshire and Moray.
However, the business also said that maintaining the overall balance between supply and demand in raw milk “continues to provide both opportunities and challenges”.
It added that margins remain tight for the business, with full-year pre-tax profit of £1.3m, down from £1.43m, which it said mirrored challenges faced across the dairy industry.
Graham said: “Despite the challenging backdrop of balancing supply and demand of raw milk prices, we have made significant progress throughout the year in relation to key elements of our strategy.
“We are well-positioned to take advantage of upcoming opportunities in the market place whilst at the same time looking to improve efficiency and profitability.”
The business also noted that as it targets further growth and innovation, it is currently working in partnership with Mactaggart & Mickel Homes to deliver a 600-home development enabling the development of a £20m+ national dairy centre.
“These developments require the support of the Scottish Government,” the dairy firm said, adding that expanding its business “will help to further support Scottish dairy farmers and give the country’s homegrown dairy industry a competitive advantage”.
Graham added: “The centre, which represents the single biggest investment in Scotland’s dairy sector in 30 years, will be home to scientists, researchers and food technicians, and will help put us, and Scotland, at the forefront of change.”
The two firms earlier this year claimed their plans would have “massive benefits” for Scotland, helping tackle the housing shortfall, and boost the dairy industry, creating 400 jobs.