Advances in information technologies have made network data increasingly frequent in a spectrum of big data applications, which is often explored by probabilistic graphical models. To precisely estimate the precision matrix, we propose an optimal model averaging estimator for Gaussian graphs (MAEGG). We prove that the proposed estimator is asymptotically optimal when candidate models are misspecified and achieves sample consistency when at least one correct model is included in the candidate set. Furthermore, numerical simulations and a real data analysis on yeast genetic data were conducted to illustrate that the proposed method is promising.