Clamped fiber Bragg grating (FBG) sensors have been widely applied in engineering strain measurements due to their advantages of high flexibility and efficiency. However, due to the existence of the interlayer, the strain measured by the encapsulated FBG sensor is not equal to the strain of the host material, which causes strain measurement errors. In this paper, the strain transfer analysis of a clamped FBG sensor based on the shear-lag theory is conducted to improve the accuracy of strain measurements. A novel theoretical model for the axial strain distribution of a clamped FBG sensor is proposed. It is also discussed how the gauge ratio and interlayer thickness affect the strain transfer rate. The accuracy of the proposed theoretical model is verified by experimental tensile tests. The theoretical value of the strain transfer rate matches well with the tested value.