Would you trust Google or Amazon to pick you the perfect avocado? The CEO of Instacart wouldn't.

"When you order your groceries, we connect you to one of our thousands of personal shoppers in our network who go to existing stores such as Whole Foods, Costco and many more, and pick up your groceries and deliver them to you within one hour," Apoorva Mehta, the founder and CEO of Instacart, told CNBC's "Fast Money" on Thursday.

"We don't hold any inventory, we don't have any warehouses, we don't have any trucks," he said.

Grocery delivery has turned into a competitive sport between internet giants Amazon and Google, but Mehta said that isn't intimidated by what those household names can offer.

Instacart hires individual contractors with their own smartphones and cars to do its shopping. All groceries are purchased from local stores and delivered within one hour or more, depending on the request.

"There are two types of competitors that we have, ones that are infrastructure-heavy and ones that are infrastructure-light," said Mehta. "AmazonFresh, Fresh Direct, Peapod—those are the infrastructure-heavy companies. When you order from those companies, you get a limited selection, only the selection that's available in their warehouses. While on Instacart you can order from all of the stores in your city. Also, because they have trucks that they have to drive around, the best they can do is next-day delivery, which is terrible from the customer's point of view. With Instacart you can get instant delivery."

Google Shopping Express is also stepping into the hunger games by offering delivery—mainly non-perishables—from names like Target, Fairway, Walgreens and Staples.

"Then there are infrastructure-light companies, like Google Shopping Express. They don't do grocery delivery. They don't do fresh groceries," Mehta said. "So while we agree that they do have deeper pockets, our products are way better."

—By CNBC's Leanne Miller