Its regular quarterly survey showed three-fifths of firms expect to grow in the next 12 months.
All sectors reported they had a positive outlook for the seventh quarter in a row.
North East England reported the most improved attitude, although the South East was most positive overall.
The report chimes with official figures from the Office for National Statistics which showed the economy had grown by 3.2% in the second quarter of this year compared to the same period last year.
International bodies from the International Monetary Fund to the OECD have said that the UK is likely to remain the fastest growing developed economy for the near future.
The FSB’s national chairman, John Allan, said: “We’re seeing record breaking confidence from our members which suggests small firms will continue to spearhead the UK’s recovery.
“We want policy makers to lock in this optimism and continue to back the self employed and small businesses. As we head in to party conference season, we’ll be looking to all the political parties to spell out what they will do to encourage job creation, investment and reward entrepreneurs in the next Parliament.”
The FSB said one third of businesses surveyed expect an increase in turnover in the next quarter and almost a fifth expect higher profits.
The most confident sector was financial services.