The core concept of software-defined network (SDN) is the separation between control plane and date plane. SDN provides a programmatic interface to network control, significantly simplifies network management and improves the efficiency of network utilization. To further improve network performance, scalability and reliability, it is recommended to deploy multiple controllers in SDN. However, network performance would degrade if operators randomly deploy the controllers, especially in the case of failure, e.g., router crashes, fiber cuts, etc. In this paper, we try to optimally place controllers while taking network failures into account. First, we formally define two problems, 1) Controller Placement under Comprehensive Network States (CPCNS) problem; and 2) Controller Placement under Single Link Failure (CPSLF) problem. Secondly, We propose a network states traversal based algorithm, which optimally solve the problem; and further propose another greedy-based algorithm, which can solve the problem in polynomial time. Finally, we evaluate the algorithms using real topologies and empirical data. The results indicate that the new controller placement strategies can significantly improve the performance when link failures happen.