The end-bonding fiber Bragg grating (FBG) sensors have many advantages such as no multiple peaks, no direct force in grating area and all points suffering the same stress, which are widely used to the packaging of substrate-type, clamp-type and other types of sensors. However, the shear deformation in the adhesive layer results in the difference between FBG strain and matrix strain, and thus the strain measurement error is introduced. In the practical applications, it is necessary to precisely obtain the function relationship between the FBG strain and the matrix strain under the influence of the shear deformation in the adhesive layer to improve the measurement accuracy of strain. For this purpose, the strain transfer equation of end-bonding FBGs based on linear viscoelasticity is derived and the average strain transfer models between fiber grating and matrix under instantaneous response and quasi-static response are developed. The parameters that influence the average strain transfer rate are discussed and analyzed. The influence law of the adhesive layer parameters with which the grating is obviously superior to that of a grating-bonding FBG sensor is demonstrated. The validity of the theoretical equation is verified by the simulation by the finite element method, and the proposed model provides a theoretical basis for the design and application of end-bonding FBG strain sensors.