Time travel is not only possible. It's happening now.
Everytime one of us accelerates or steps on the gas pedal and overpasses another car, we are travelling faster both in space and in time. We became just a bit younger than the drivers behind us, even if only a trillionth of a fraction of a second, the the change is there. We are always travelling to the future.
The only time travel that is debatable is travelling BACK in time. That's a complete different story.
As for the Grandfather Paradox, I don't see any problem with that.
It reads: there's no possibility of going back in time because the traveller COULD kill his grandfather or change something in ways that would prevent him from being born.
The problem with this is that it would only make sense in an non-deterministic Universe. In a deterministic Universe, everything that happened would have happened anyway. If you go to the past and try to kill your grandfather, you won't succeed. If you make a million trips to the past with all the necessary equipment to asure you'll succeed in killing your grandfather, you'll fail a million times. It may go against our intuitions and our sacred belief in an open Universe (a non-deterministic Universe) and our equally sacred belief in free will, but just because we believe we have free will and that free will is an integral part of an open Universe, doesn't mean there are such things. In a deterministic Universe you may even shoot your grandfather in the head, only to find out that he was NOT your grandfather and not your mother's or father's father. You just killed the wrong person. You thought he was your grandfather but he never was. As long as it's determined that you won't be able to kill your grandfather or change anything that would result in a paradox, like you not existing, you'll be allowed to travel back in time because everything you do, will only result in things that have already happened in the future. You always wondered how your mother came across a chest with gold bars and you and your family became millionaires. One day you go to the past, you steal a chest with gold bars, bury it somewhere, send a letter to your unborn mother, she reads it years later, before you were born, she finds it and you are born to a rich family. You didn't know how she found the gold until, years later, you got involved with time travel experiments, you went to the days of the American Civil War, you stole the gold bars and buryed in a safe place and sent a letter to to be delivered more than a century later through Western Union (like the final scene in Back to the Future II). You cannot even decide NOT to steal the gold because your actions are not driven by a delusive free will.