A parallel structured optical fiber Fabry-Perot interferometer sensor is proposed and demonstrated for refractive index and strain sensing with low temperature cross sensitivity. The device consists of two Fabry-Perot cavities fabricated by a femtosecond laser: one is inscribed in the fiber surface waveguide and used for sensing, and the other one is located in the fiber core for referencing. Part of the light propagating in the fiber core can be directed to the fiber surface waveguide via an X coupler. Because of the evanescent field, the light traveling along the fiber surface waveguide interacts with the surrounding medium and enables external refractive index sensing. The measurement sensitivity of the device is enhanced due to the Vernier effect associated with the parallel structured two Fabry-Perot interferometers. The sensitivities of ∼843.3nm/RIU and ∼101.8pm/µε have been obtained for refractive index and strain, respectively, and the corresponding temperature cross sensitivities are ∼9.6×10-6RIU/∘C and ∼7.956×10-2µε/∘C, respectively. The device is featured with high robustness, compact size, and large sensitivity.