In this paper, we propose a robust sensor placement methodology, which takes into consideration of possible sensor failure encountered in sensory systems. Although the optimal sensor placement problem has been studied for decades, previous works assumed a fully functioned sensory network. In real practice, sensor failure is commonly encountered, and this may seriously degrade the performance of the sensor network. The proposed method considers the impact of sensor failure on the performance of the sensor configurations so that the designed configuration is robust against sensor failure. For this purpose, we define the robust information entropy to quantify the uncertainty of the identified model parameters with consideration of sensor failure. Furthermore, we propose a tailor-made heuristic sequential search algorithm to enhance the computational efficiency. The proposed methodology is illustrated by designing the robust sensor configuration for a 20-story shear building and a space truss. Moreover, a case study using the in-field measurements of the Canton Tower is presented to demonstrate the performance of the proposal methodology.