The company said sales had increased by 30% in the four months to June.
The trading statement pushed up Asos shares 3.7%, reaching a two-year high.
Chief executive Nick Beighton said the company now expected full-year sales growth "at the upper end of the 20-25% (guided) range," and was "confident" of hitting pre-tax profit targets.
In a conference call, he said that there would be a medium-term benefit to the company from the weaker pound.
Sterling has slumped to around $1.30 from almost $1.50 on 23 June before the vote to leave the European Union. A weaker pound enables UK based retailers to be more competitive in overseas markets.
Sales were £500.5m for the four months to June compared with £386m last year, with the number of active customers increasing by 24% to 12 million.
Sales were strong both in the UK, which posted a rise of 28% to £203m, and internationally, which rose 31% to £297m.
Asos confirmed the closure of its Chinese business, originally announced April, saying that this would enable it to invest £2m elsewhere and remove a drag on earnings.
Asos was set up in 2000 and was an early entrant into online fashion retailing, but in recent years it has faced stiff online competition from High Street retailers as well as UK and European competitors.
Online fashion retailer Asos is predicting full-year sales growth at the top end of forecasts after posting stronger-than-expected trading.