Red Hat has more than 300,000 subscribers to its Enterprise Linux support service.
The company also reported revenue of $41.6m (£23m) and net income of $10.7m for the quarter, which ended 31 May.
Red Hat added 98,000 new subscriptions during the quarter, up 13% from the 87,000 reported during the fourth quarter of 2003.
Enterprise customers purchased 75,000 of the subscriptions sold during the first quarter and the other 23,000 were sold to high performance computer and web hosting users.
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Red Hat also announced that its chief financial officer, Kevin Thompson, planned to step down.
The company has already begun a search for a replacement, who is expected to be hired within the next 90 days, according to Matthew Szulik, Red Hat's chief executive officer.
"We're looking for someone who has the experience of managing a larger business," he said.
Robert McMillan writes for IDG News Service