  In this paper we study perturbatively an extension of the Stelle higher
derivative gravity involving an infinite number of derivative terms. We know
that the usual quadratic action is renormalizable but is not unitary because of
the presence of a ghost in the theory (pole with negative residue in the
propagator). The new theory is instead ghost-free since an entire function (or
form factor) is introduced in the model without involving new poles in the
propagator. The local high derivative theory is recovered expanding the entire
functions to the lowest order in the mass scale of the theory. Any truncation
of the entire function gives rise to unitarity violation. The theory is
divergent at one loop and finite from two loops upwards: the theory is then
super-renormalizable. Using the modified graviton propagator, we demonstrate
the regularity of the gravitational potential in r=0.
