Yes! Plants can grow without soil! My daughter had a little cherry tomato garden where the plants just had water and light and some chemicals in the water.

Growing plants that way is called 'hydroponics.' There's a nice article about this online in Wikipedia: click here

My daughter's tomatoes didn't grow very well, because I put the wrong chemicals on it. I used chemicals for growing green things like herbs, not the ones for growing plants that will have flowers and fruit.