Using the full-vector coupled mode theory, a method for Surrounding Refractive Index (SRI) sensing with a single wavelength was proposed which is based on the core-only photoinduced birefringence of Long-Period Fiber Grating (LPFG). With a completely-polarized light near the resonant wavelength launched into the LPFG, the variation of the spherical distances between the output light polarization states for various SRIs and that for the reference SRI=1 on the Poincare sphere is investigated to identify the SRIs. The analysis indicates that the SRI sensor with a cladding radius of 20.75 μm shows a good linearity performance and high sensitivity of 0.356/RIU over the SRI measurement ranging from 1 to 1.30, which, unlike the available LPFG sensors, may be applied to the humidity and vapor sensing. Meanwhile, the analysis method is applicable to the design of other types of birefringent-LPFG sensors.