There is a strain transferring ratio between structure and fiber Bragg grating sensor for the existence of sensor’s interlayer. A strain transfer model is developed based on shear-lag theory for evaluating the interaction between the surrounding host material and a length of fiber Bragg grating sensor embedded in it, when there is an angle existence between the sensor axis and the external principal stress direction of the host material. And the general formula of average strain transfer rate is deduced at the same time. The fiber Bragg grating sensors were used to verify the theoretical results. When the angle α is 30.72°, the wavelength changes ratios of experimental results are 0.727,0.738,0.746 respectively; and the theoretical result is 0.739, the errors are less than 2%. At last, strain measured error which are induced by sensor location angle deviation is discussed. The result indicates that the strain transfer models that the fiber Bragg grating sensor under non-axial stress and axial stress are greatly different, and the measured results have some errors because of the angle location error of fiber Bragg sensors.