Box shares went on sale at over $20.20 (£13.46) on the New York Stock Exchange today.
The 12.5 million shares were due to be priced at $14 each, according to underwriters familiar with the listing, but they are now trading at over $24 each.
Earlier this month Box said shares would be sold for between $11 (£7) and $13 (£9).
The file-sharing firm first filed for an IPO in March 2014, announcing that it wanted to raise $250 million (£166 million).
However, it has stalled by nearly a year following uncertainty in the market.
In a bid to support its excessive spending habits ahead of the IPO, Box raised an additional $150 million (£93 million) in venture capital funding.
The success of today's offering depends on how much investors focus on Box's excessive spending habits and "internal issues", according to Alastair Micthell, CEO of rival firm Huddle.
Dropbox, another rival, announced yesterday that it is expanding to the UK and opening an office in London's Fitzrovia district, which happens to be a short walk from Box's office in Mayfair.