Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not clearly understood. Here we study the impact of correlated inter-layer couplings on the network robustness of coupled networks using percolation concept. We found that the positive correlated inter-layer coupling enhaces network robustness in the sense that it lowers the percolation threshold of the interlaced network than the negative correlated coupling case. At the same time, however, positive inter-layer correlation leads to smaller giant component size in the well-connected region, suggesting potential disadvantage for network connectivity, as demonstrated also with some real-world coupled network structures.