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We consider the gradient field model in $\left[ -N,N\right] ^{2}\cap\mathbb{Z}^{2}$ with a uniformly convex interaction potential. Naddaf-Spencer\cite{NS} and Miller \cite{Mi} proved that the macroscopic averages of linearstatistics of the field converge to a continuum Gaussian free field. In thispaper we prove the distribution of $\phi(0)/\sqrt{\log N}$ converges uniformlyto a Gaussian density, with a Berry-Esseen type bound. This implies thedistribution of $\phi(0)$ is sufficiently `Gaussian like' between $[-\sqrt{\log N}, \sqrt {\log N}]$.

Local central limit theorem for gradient field models