Shares shot up from their 25.50 euros starting price to trade at 27 euros ($30.81) just after the market opened at 0700 GMT, before falling back to 26.17 euros by 0830.
The starting price would have valued Delivery Hero at around 4.4 billion euros.
"This is a great day. We want to continue to grow very quickly. This is just the beginning," chief executive Niklas Oestberg told journalists on the trading floor.
Just under 1.0 billion euros of stock was on offer, split between newly-issued shares and existing shares from earlier shareholders.
Created in 2011, the firm claims a presence in more than 35 countries worldwide and 6,000 employees, as well as thousands of delivery drivers.
In 2016, Delivery Hero continued to lose money despite boosting revenue 75 percent to 347 million euros.
The company says that it aims to break even by 2019.
Around 35 percent of Delivery Hero is presently owned by Berlin startup incubator Rocket Internet, itself listed on the Frankfurt stock exchange.