The Great Red Spot at about latitude 22oS of Jupiter has been observed for hundreds of years, yet the driving mechanism on the formation of this giant anticyclone still remains unclear. Two scenarios were proposed to explain its formation. One is a shallow model suggesting that it might be a weather feature formed through a merging process of small shallow storms generated by moist convection, while the other is a deep model suggesting that it might be a deeply rooted anticyclone powered by the internal heat of Jupiter. In this work, we present numerical simulations showing that the Great Red Spot could be naturally generated in a deep rotating turbulent flow and survive for a long time, when the convective Rossby number is smaller than a certain critical value. From this critical value, we predict that the Great Red Spot extends at least about 500 kilometers deep into the Jovian atmosphere. Our results demonstrate that the Great Red Spot is likely to be a feature deep-seated in the Jovian atmosphere.