Structural health monitoring systems are being recognized as effective tools to minimize maintenance costs for civil infrastructures. Recently, many damage evaluation methods for the systems have been proposed. For example, natural frequencies were used for global monitoring, and strain measurement for local monitoring. In this study, a novel monitoring system that measures two physical values simultaneously, acceleration and strain, by a single sensor is proposed. At first, a hybrid FBG sensor for monitoring strain and acceleration is proposed. The sensor consists of an FBG element and a mass to form a vibration system. Then, a monitoring system using the hybrid FBG sensor and support vector machines is proposed. Many damage scenarios for a moment-resistant frame were tested. The results show that the sensitivities of strain and natural frequency are significantly different. It is confirmed that combined use of acceleration and strain measurement enhances the performance of the system.