The three college students who started the petition say they are not opposed to the app's functions, but don't want to see the hula dance - a beloved cultural art form - exploited.
"My culture is more than a tourist destination," said Kelly Luis, a student at Columbia University.
"It is more than a place to go for the summer. It's more than just sexy hula girls on the beach. There is a culture there."
As of Wednesday, nearly 700 people signed the petition at change.org.
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The petition notes that the arrival of Europeans exposed Native Hawaiians to diseases such as gonorrhoea and syphilis.
It's not clear why the app is named Hula. It was originally called Qpid.me, but the name changed about six months ago.
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Nani Kauka, a hula teacher from Kailua, said this was another example of the Hawaii culture being exploited and misunderstood.
"I don't like it," she said.
"Why don't they call it ballet or jazz?"
- AP