No, you will accelerate due to gravity all the way to the centre at which point you will start to decelerate due to the same gravity. The rate of acceleration will decrease based on the amount of Earth's mass "behind" you. You will have zero acceleration at the centre of the Earth, but a heck of a lot of speed.
I was going to work out the maximum speed, because I suspect that the heat from air resistance would incinerate you, probably before the heat of the core did.