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It is shown that any smooth strictly convex global solution of$$\det(\frac{\partial^{2}u}{\partial \xi_{i}\partial \xi_{j}}) = \exp\left\{-\sum_{i=1}^n d_i \frac{\partial u}{\partial \xi_{i}} - d_0\right\},$$where $d_0$, $d_1$,...,$d_n$ are constants, must be a quadratic polynomial.This extends a well-known theorem of J\"{o}rgens-Calabi-Pogorelov.

A Rigidity Theorem for Affine K\"ahler-Ricci Flat Graph