Revenues rose 19 per cent to £1.26bn, with like-for-like sales – which do not include figures from new stores – going up by eight per cent.
The chain, which has 196 European stores, will open another six this year as part of its expansion plans.
Chief executive George Weston said Primark was going "from strength to strength".
He added: “The investments made in recent years are now delivering very satisfying returns throughout the group.”
ABF also owns brands including Kingsmill and Twinings as well as the Silver Spoon sugar business.
Underlying pre-tax profits for the entire group soared by a fifth to £331m for the six months to 27 February.