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Link prediction is a fundamental problem with a wide range of applications in various domains, which predicts the links that are not yet observed or the links that may appear in the future. Most existing works in this field only focus on modeling a single network, while real-world networks are actually aligned with each other. Network alignments contain valuable additional information for understanding the networks, and provide a new direction for addressing data insufficiency and alleviating cold start problem. However, there are rare works leveraging network alignments for better link prediction. Besides, neural network is widely employed in various domains while its capability of capturing high-level patterns and correlations for link prediction problem has not been adequately researched yet. Hence, in this paper we target atlink prediction over aligned networks using neural networks. The major challenge is the heterogeneousness of the considered networks, as the networks may have different characteristics, link purposes, etc. To overcome this, we propose a novel multi-neural-network framework MNN, where we have one individual neural network for each heterogeneous target or feature while the vertex representations are shared. We further discuss training methods for the multi-neural-network framework. Extensive experiments demonstrate that MNN outperforms the state-of-the-art methods and achieves 3% to 5% relative improvement of AUC score across different settings, particularly over 8% for cold start scenarios.