Matrix completion is one of the key problems in signal processing and machine learning, with applications ranging from image processing and data gathering to classification and recommender systems. Recently, deep neural networks have been proposed as latent factor models for matrix completion and have achieved state-of-the-art performance. Nevertheless, a major problem with existing neural-network-based models is their limited capabilities to extend to samples unavailable at the training stage. In this paper, we propose a deep two-branch neural network model for matrix completion. The proposed model not only inherits the predictive power of neural networks, but is also capable of extending to partially observed samples outside the training set, without the need of retraining or fine-tuning. Experimental studies on popular movie rating datasets prove the effectiveness of our model compared to the state of the art, in terms of both accuracy and extendability.