International Airlines Group saw traffic rise by 7.4% in March measured in revenue passenger kilometres over the same month last year.
This came as overall capacity for the British Airways, Iberia and Vueling owner increased by 4.8%.
The group reported a 5.4% year-on-year increase in premium traffic for the month.
BA started Airbus A380 services to San Francisco from Heathrow at the end of March, adding 6,000 more seats a month between the two cities.