The precision of the encapsulated fiber optic sensor embedded into a host suffers from the influences of encapsulating materials. Furthermore, an interface transfer effect of strain sensing exists. This study uses an embedded basalt fiber-encapsulated fiber Bragg grating (FBG) sensor as the research object to derive an expression in a multilayer interface strain transfer coefficient by considering the mechanical properties of the host material. The direct impact of the host material on the strain transfer at an embedded multipoint continuous FBG (i.e., multiple gratings written on a single optical fiber) monitoring strain sensor, which was self-developed and encapsulated with basalt fiber, is studied to present the strain transfer coefficients corresponding to the positions of various gratings. The strain transfer coefficients of the sensor are analyzed based on the experiments designed for this study. The error of the experimental results is when the strain is at and below. Moreover, the measured curves almost completely coincide with the theoretical curves. The changes in the internal strain field inside the embedded structure of the basalt fiber-encapsulated FBG strain sensor could be easily monitored. Hence, important references are provided to measure the internal stress strain of the sensor.