Bosses said the airport had enjoyed 13 months of growth with a bumper June, which saw a 17% year-on-year increase.
More than 6,000 people travelled from the airport, near Rhoose, to France for the Euro 2016 football championship.
Debra Barber, managing director and chief operating officer, said it had been an "exciting time".
The 28% rise was based on the rolling annual total of travellers from June 2015 to June 2016.
Figures released in April 2015 had shown a fall of 38,000 (3.6%) in 2014.
After announcing the new figures on Tuesday, Roger Lewis, chairman of the airport, said: "Today we are sending a signal to the world that Wales is well and truly open for business."
He said Cardiff Airport was the "fastest growing airport in the UK that regularly handles over one million passengers" and added the operators "intend to expand our activities".
The Vale of Glamorgan airport provided the stage for the Welsh football team's departure for Euro 2016 on 4 June, with Chris Coleman's side receiving a hero's welcome on their return on Friday, after reaching the semi-finals.
Cardiff Airport was bought by the Welsh Government for Â£52m in March 2013 and operated at arms' length since then.
The move was later criticised by opponents after a KPMG report suggested the government had paid double an initial valuation.
Mr Lewis told BBC Radio Wales he had started "initial discussions" with potential private sector investors, but any sale would still be some years away.
He also said a target of two million passengers a year was within reach.
The number of passengers flying from Cardiff Airport has grown by 28% to 1.3 million in the last year, according to new figures.