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.

The fire in Barn End Lane, Wilmington, was reported at about 07:40 BST, Kent Fire and Rescue Service said.
At its peak, eight fire crews tackled the blaze in one of the flats, which spread smoke to neighbouring flats. The cause of the fire is not yet known.
The man was pronounced dead at the scene. Eight people were taken to hospital after the fire, South East Coast Ambulance (Secamb) said.
Secamb earlier said nine people were taken to hospital but has since revised its figure.
The Kent, Surrey and Sussex Air Ambulance and nine ambulances were called to the scene.
For a time, Darent Valley Hospital in Dartford asked patients not to attend its accident and emergency department, saying the hospital was dealing with a "major incident".
The Darent Valley later tweeted: "The hospital has been stood down and normal service has resumed in the A&E Department."
Fashion group Ted Baker has reported strong profits for the first half of 2016 despite challenging trading conditions.
[NEXT_CONCEPT]
A man in his 70s has died in a fire at a flat in a sheltered housing block.