A fiber-Bragg-grating-(FBG)-based sensor is a very popular fiber optic sensor due to its simplicity, mature fabrication technology, and sensitivity to a number of physical stimuli. However, due to the stiff nature of optical fiber, it is impossible to heavily stretch a FBG sensor. A stretchable sensor is highly desired in soft robotics, human motion detection, and biomedical applications, which could involve motions like tension, bending, and twisting. In this Letter, we demonstrate a stretchable FBG-based fiber optic sensor by embedding a FBG-written optic fiber sinusoidally in a soft silicone film at an off-center position. This unique structure enables 30% of elongation in length that facilitates tension, bending, and twisting measurement.