We propose a variant of hybrid inflation which is applicable in a wide class of supersymmetric grand unified models. The observed temperature perturbations of cosmic background radiation can be reproduced with natural values of the parameters of the theory and a grand unification scale which is consistent with the unification of the minimal supersymmetric standard model gauge couplings as measured at LEP. The termination of inflation is smooth and does not produce any topological defects. Finally, we present a specific supersymmetric model where our smooth hybrid inflationary scenario is realized.

15 pages, latex, to appear in Phys. Rev. D (Rapid Com.)