The issue about cascading failures of interdependent networks is a hot research field based on the current complex network basic theories. This paper mainly researches methods for improving robustness of interdependent networks. At first, a model of interdependent network cascading failures was established to carry out robustness analysis of three different interdependent networks including BA-BA, WS-WS and ER-ER. Then, methods for improving robustness of interdependent networks under random attacks and targeted attacks were researched respectively. (1)Under random attacks, based on the overall idea of network addition, the paper summarized four common methods for improving robustness of a simple complex network, including random addition, low-degree node addition, low-betweenness node addition and addition based on algebra connectivity. After that, according to inherent characteristics of interdependent networks, the paper put forward an interdependent network addition algorithm based on internal similarities. It is shown in cascading failure simulation calculation results of three interdependent coupling networks, that the method put forward in this paper can most effectively improve robustness of interdependent networks under random attacks. (2)Based on the overall idea of protecting key nodes under targeted attacks, the paper put forward a method for analyzing key nodes of interdependent networks based on natural connectivity. Then, under the BA-BA interdependent network, the paper analyzed this method in comparison with the commonly approved Max-Cas algorithm. It is shown in simulation calculation results that, the method put forward in this paper can more obviously improve robustness of an interdependent network under targeted attacks and can be applied flexibly.