Network alignment and network completion are two fundamental cornerstones behind many high-impact graph mining applications. The state-of-the-arts have been addressing these tasks in parallel. In this paper, we argue that network alignment and completion are inherently complementary with each other, and hence propose to jointly address them so that the two tasks can benefit from each other. We formulate it from the optimization perspective, and propose an effective algorithm iNEAT to solve it. The proposed method offers two distinctive advantages. First (Alignment accuracy), our method benefits from higher-quality input networks while mitigates the effect of incorrectly inferred links introduced by the completion task itself. Second (Alignment efficiency), thanks to the low-rank structure of the complete networks and alignment matrix, the alignment can be significantly accelerated. The extensive experiments demonstrate the performance of our algorithm.