We demonstrate a fiber Bragg grating (FBG) strain sensor with optical frequency combs. To precisely characterize the optical response of the FBG when strain is applied, dual-comb spectroscopy is used. Highly sensitive dual-comb spectroscopy of the FBG enabled strain measurements with a resolution of 34 nε. The optical spectral bandwidth of the measurement exceeds 1 THz. Compared with conventional FBG strain sensor using a continuous-wave laser that requires rather slow frequency scanning with a limited range, the dynamic range and multiplexing capability are significantly improved by using broadband dual-comb spectroscopy.