Lithium-ion batteries show promise for use in energy storage applications in power stations. There are two current concerns with power stations: cost and safety. The cost problem is being gradually solved, but safety is always a challenge in the large-scale utilization of lithium-ion batteries. Battery management systems, which rely mainly on voltage and current monitoring, are an effective way to ensure the safe operation of batteries. Strain is an equally critical parameter for battery state monitoring to improve safety and utilization efficiency. In this paper, we present a new high precision method of strain monitoring based on a fiber Bragg grating sensor. The sensor consists of a fiber Bragg grating and a sensitivity-enhancing mechanism, making it more sensitive than the bare fiber Bragg grating sensor. A comparison test between our proposed sensor and bare fiber Bragg grating sensor have confirmed its performance in monitoring the strain in a battery. Our investigation into the relationship between strain and state-of-charge/depth-of-discharge suggests that the strain increases as the state-of-charge increases, and decreases as the depth-of-discharge increases. This method is a promising tool for providing strain data on power batteries for battery management systems.