A fiber surface plasmon resonance (SPR) sensor is widely used in high-sensitivity refractive index measurement, but there is less research on curvature measurement. In this paper, a single-mode fiber curvature sensor based on SPR is designed and fabricated. By employing bending, the transmitted light in the fiber core leaks into the cladding. A 50 nm gold film is coated outside the cladding, and the evanescent field of the cladding after bending contacts the gold film to cause SPR. When the curvature changes, the coupled cladding mode and intensity are different; that is, the SPR incident angle and evanescent field intensity are different, so as to realize the dual parameters of SPR resonance wavelength and depth of the resonance valley changing with curvature. By experiments, the influence of different cutoff wavelengths of single-mode fiber on the performance of the sensor is studied. The testing results indicate that with the decrease in cutoff wavelength of the single-mode fiber, the valley depth sensitivity of the sensor increases, and the half height width (FWHM) decreases. When the cutoff wavelength of the single-mode fiber is 630 nm, the valley depth sensitivity of the sensor is 0.0088a.u/m-1, the wavelength sensitivity is 0.26nm/m-1, and the average FWHM is only 21 nm. The proposed single-mode fiber curvature sensor based on SPR has a narrow FWHM and an opening threshold. It can also realize no opening threshold by introducing a coreless fiber, which provides a new solution, to the best of our knowledge, for the diversified detection of fiber SPR sensors.