A fiber Bragg grating strain sensor, whose reflection bandwidth is insensitive to temperature, is presented. The cross-sectional area is designed to change linearly. Under axial stress, there is a linear relationship between stress and average strain. Experimental results show that when temperature increases, reflection center wavelength shifts to longer wavelength, and there is a good linear relationship between center wavelength and temperature. When stress increases, reflection center wavelength shifts to longer wavelength, and reflection bandwidth increases. There are good linear relationships between reflection center wavelength and stress as well as reflection bandwidth and stress.