Based on the Sagnac effect, the small changes in thermally induced stresses and microcosmic size of optical fiber coil can cause the drift of the Shupe error and scale factor of fiber optic gyroscope (FOG). As polymer functional resin represents a high proportion in optical fiber coil, its physical and chemical properties determine largely the thermally induced stresses and dimensional stability of the coil, thus influencing the performance of FOG. Given the demands for the long-term stability and temperature characteristics of FOG, this paper studies the influence of molecular chain structure and thermal conductivity of polymer functional resin for optical fiber sensing on FOG. The experimental results suggest: high thermal conductivity can reduce the thermal induced stresses of polymer functional resin of reticular molecular structure, greatly improving the zero bias stability of FOG at all temperature; hyperbranched molecular structure reports outstanding creep-resistant characteristics thanks to the significantly reduced internal free volume of optical fiber coil after encapsulation and insignificant dimensional changes at all temperatures, thus ensuring long-term stability of the scale factor of FOG.