In the six months to 13 August, sales climbed 14.4% to Â£259.5m, with profits rising 20.5% to Â£21.5m.
This was despite rival retailers struggling due to unseasonal weather.
"This is the company's first update since Brexit, and is a strong showing," said George Salmon, an analyst at Hargreaves Lansdown.
"The second half of the year is more important to Ted Baker than the first, nonetheless the news that sales growth remains robust provides reassurance that the group can continue to thrive, even in challenging times."
The company, which opened its first store in Glasgow in 1988, now has 470 outlets worldwide selling fashion and accessories.
It grew in all its markets, with retail sales in the UK and Europe - its biggest market - up 8.5%. In North America sales climbed 28.7% and they were 15.8% higher in Asia.
Online sales meanwhile leapt 29.7% as the firm invested in web design, personalised content and language-specific websites.
Brands such as Next and H&M have reported below-forecast results this year, with sales hit by colder weather in March and April this year.
However, Zara-owner Inditex reported strong first-half profits, driven partly by rising online sales.
Fashion group Ted Baker has reported strong profits for the first half of 2016 despite challenging trading conditions.