Aims. The aim of this work is to obtain the cratering rate on Pluto and to estimate the size distribution of the population in the inner trans-Neptunian region. Methods. We find the intrinsic collisional probability and the mean collision velocity for the interaction between Pluto and the projectile population crossing its orbit, using the L7 Synthetic Model from the CFEPS Project. The size distribution of this population is found using the smallest satellite of Pluto, Styx, as a constraint, because it survives the collisional process for the solar system age. Results. We find that the mean intrinsic collisional probability and mean collision velocity between Pluto and the projectile population are (Pi) = 1.3098 × 10-22 km-2 yr-1 and (Vcol) = 2.005 ± 0.822 km s-1. If the projectile sample is separated between Plutinos and non-Plutinos and the intrinsic collisional probability of these sub-populations are taken into account, we find a ratio of approximately 20:1 in favor of non-Plutinos resulting in the greatest contribution to the cratering rate on Pluto. The projectile population for the inner trans-Neptunian belt is characterized using a double power-law mean-size distribution with exponents qA = 3.5 and qB = 5.14 for the small and large size end of the population, respectively, and break radius at rb = 11.86 km or 7.25 km for mean densities of the projectiles ρ1 = 1.85 g cm-3 and ρ2 = 1 g cm-3. With this mean-size distribution we find that an object with radius of ~28 km produces a crater in Pluto with a diameter of ~250 km in a time larger than the solar system age, indicating that this kind of large structure has a very low probability of occurrence.