Apple applied to use the name in Brazil in 2007, when Gradiente had yet to launch any products of its own under the name, due to poor financial health.
But just as its patent on the name was about to expire, Gradiente unveiled in December 2012 its iPhone, which costs about a third of the price of Apple's latest model.
The institute said its decision will be officially published February 13 in its Intellectual Property magazine.
Neither Gradiente nor Apple have commented on the decision, which Apple can still appeal, unless it comes to an agreement with Gradiente.
Apple faced a similar obstacle in the US, where Cisco Systems owned the rights to the iPhone brand and reached an agreement with Apple.
Additionally, Apple's iPad brand was owned by Proview Technology, which sold the rights to Apple for $60 million.