Asphalt pavement is vulnerable to random damage, such as cracking and rutting, which can be proactively identified by distributed optical fiber sensing technology. However, due to the material nature of optical fibers, a bare fiber is apt to be damaged during the construction process of pavements. Thus, a protective layer is needed for this application. Unfortunately, part of the strain of the host material is absorbed by the protective layer when transferring the strain to the sensing fiber. To account for the strain transfer error, in this paper a theoretical analysis of the strain transfer of a three-layered general model has been carried out by introducing Goodman’s hypothesis to describe the interfacial shear stress relationship. The model considers the viscoelastic behavior of the host material and protective layer. The effects of one crack in the host material and the sensing length on strain transfer relationship are been discussed. To validate the effectiveness of the strain transfer analysis, a flexible asphalt-mastic packaged distributed optical fiber sensor was designed and tested in a laboratory environment to monitor the distributed strain and appearance of cracks in an asphalt concrete beam at two different temperatures. The experimental results indicated that the developed strain transfer formula can significantly reduce the strain transfer error, and that the asphalt-mastic packaged optical fiber sensor can successfully monitor the distributed strain and identify local cracks.