It is tempting to imagine that an object could exist without gravity if it was placed outside the Earth's atmosphere and 'pull'. After all, objects and people inside space craft that have left the Earth float and have little control over reaching other objects.
However, Einstein's theory of relativity asserts that gravitational forces exist between every pair of objects in the universe. If an object has mass, it must have gravity. There are advanced scientific discussions about whether any conditions could theoretically exist that would alter this, or rather, where it would not apply, but I think you have to get your first degree in Physics first before worrying about the question.