During the preheating process at the end of inflation the amplification of
field fluctuations can lead to the amplification of curvature perturbations
. If the curvature perturbations on small scales are sufficiently large, pr
imordial black holes (PBHs) will be overproduced. In this paper we study PB
H production in the two-field preheating model with quadratic inflaton pote
ntial. We show that for many values of the inflaton mass m, and coupling g,
small scale perturbations will be amplified sufficiently, before back reac
tion can shut off preheating, so that PBHs will be overproduced during the
subsequent radiation dominated era.