Manjit's Kitchen in Kirkgate Market is run by Manjit Kaur, from Chapeltown, who began cooking Indian street food for delivery from her home back in 2010.
She and her husband Michael then converted an old horsebox into a food truck which they would take to festivals, events and weddings.
In 2016 she opened Manjit's Kitchen in the market's food hall, offering vegetarian and vegan Indian cuisine.
The cafe has been a huge success, and Manjit is now looking to expand to new premises so she can continue to trade in the evenings.
She has started a Kickstarter campaign with the aim of raising Â£40,000 from public donations.
Anyone who contributes will receive rewards such as meals at the new restaurant or catering for a private event.
The business now employs eight staff and this summer won the Best Street Food title at the BBC Food and Farming Awards.
So far, Â£5,000 has been pledged from backers. Manjit herself has already raised a third of the projected opening costs.
"We have learned lots running the cafe and are now ready to take this learning forward and open another place," said Manjit.
"As we are based in the market, the cafe closes at 5pm. We have therefore built the cafe on lunchtime trade only. We now want to build another place we can open in the evenings too.
"I want to employ more people and continue to develop our style of Indian vegetarian food. We can develop our drinks offer by expanding our partnerships with local breweries and creating a cocktail menu
"I believe a thriving, independent business scene is important to a city and we want to be part of that. We work closely with local charities and through our business we want to make Leeds a better place."
The cash raised by the Kickstarter funding campaign will be used to purchase kitchen equipment and fit out a new site, as well as for leasing, surveying, legal and licensing fees.
"I don't want to go to the banks. I went once and it wasn't much fun. With your help and support we can make this happen."
Manjit is currently viewing potential sites for the new venture.
Kickstarter refunds donors if the fundraising target is not met by a specified deadline - which in this case is the end of October.
Anyone pledging more than Â£10 will receive a voucher to spend at the restaurant when it opens, while donors who give more than Â£30 will get a free meal for two. Other rewards include an invitation to the launch night and a visit from the horsebox to a private party for up to 100 guests.