Because Pluto's orbit is elliptic, there are two answers:
Farthest distance is about 7,4 bilion km.
Closest distance is about 4,4 bilion km
Pluto is about 39 times as far from the sun as Earth is. Its average distance from the sun is about 3,647,240,000 miles (5,869,660,000 kilometers). Pluto travels around the sun in an elliptical (oval-shaped) orbit. At some point in its orbit, it comes closer to the sun than Neptune, the outermost planet. It stays inside Neptune's orbit for about 20 Earth years. This event occurs every 248 Earth years, which is about the same number of Earth years it takes Pluto to travel once around the sun. Pluto entered Neptune's orbit on Jan. 23, 1979, and remained there until Feb. 11, 1999. As it orbits the sun, Pluto spins on its axis, an imaginary line through its center. It spins around once in about six Earth days.