Two kinds of photonic crystal fiber (PCF) sensors based on surface plasmon resonance (SPR) with silver nano-continuous gratings (i) and (ii) are designed. The coupling characteristics and sensing properties are analyzed numerically by the finite element method (FEM). The results show that the proposed sensor based on silver nano-continuous grating (i) can achieve better performance than that of the sensors based on silver nano-continuous grating (ii) and plane silver film structures. When the segmented number is 50 and segmented angle is 0.5°, a wavelength sensitivity of the proposed sensor with silver nano-continuous grating (i) is obtained as high as 13,600 nm/RIU in the refractive index (RI) range from 1.330 to 1.365, corresponding to a maximum RI resolution of 7.35×10-6 RIU, which can have promising applications in medical and environmental monitoring and biochemical detection.