Minimal supersymmetric hybrid inflation based on a minimal Kähler potential predicts a spectral index n _ { s } \lower 3.01 pt \hbox { $ \stackrel { \textstyle > } { \sim } $ } 0.98 .
On the other hand , WMAP three year data prefers a central value n _ { s } \approx 0.95 .
We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kähler potential .
Including radiative corrections using the one-loop effective potential , we show that the prediction for the spectral index is sensitive to the small non-minimal corrections , and can lead to a significantly red-tilted spectrum , in agreement with WMAP .