There may be more than 2% strain of carbon fiber composite material on solid rocket motor (SRM) in some extreme cases. A surface-bonded silica fiber Bragg grating (FBG) strain sensor coated by polymer is designed to detect the large strain of composite material. The strain transfer relation of the FBG large strain sensor is deduced, and the strain transfer mechanism is verified by finite element simulation. To calibrate the sensors, the tensile test is done by using the carbon fiber composite plate specimen attached to the designed strain sensor. The results show that the designed sensor can detect the strain more than 3%, the strain sensitivity is 0.0762 pm/με, the resolution is 13.13με, and the fitting degree of the wavelength-strain curve fitting function is 0.9988. The accuracy and linearity of the sensor can meet the engineering requirements.