A new kind of transverse-stress sensor which uses photonic crystal fiber (PCF) with dual-core structure as an optical waveguide is designed based on the surface plasmon resonance (SPR) effect. The relationship between the shift of the fundamental mode resonance peak and the transverse-stress is obtained when we build the model of the SPR coupled wave and the deformation model of the PCF structure by the vector finite element method. Results show that the wavelength shift of the resonance peak is linear with the added stress. A high measurement sensitivity is obtained when the optimal design for the cross section structure of PCF, and the number of layers, the diameter and the period of air holes are selected. This study can provide theoretical guidance for the design of PCF transverse-stress sensor based on SPR.