We propose a high-quality refractive index sensing by utilizing the characteristic guided-mode resonance (GMR) excited in a simple one-dimensional all-dielectric nano-slit array. We demonstrate a figure of merit up to 12000, which is higher than that achieved in most plasmonic refractive index sensors. We show that high-quality sensing performance can be sustained over a broadband range in near infrared region with relatively large variations in both grating depth and angle of incidence. Such a GMR-based all-dielectric sensing device with the ease of fabrication is expected to hold great promise for realizing broadband refractive index sensors with high performance and compactness.