Anapole modes supported by the well-designed dielectric nanostructure have attracted extensive concerns in the field of nanophotonic applications owing to its unique strong near-field enhancement and nonradiative far-field scattering characteristics, yet it is still difficult to achieve high Q-factor resonance features with narrow linewidth. In this work, a periodic slotted silicon nanodisk array is theoretically proposed to realize narrow linewidth and high Q-factor resonance in the near-infrared wavelength range. Through introducing the coupling between the anapole modes in the single dielectric nanostructure and the diffractive wave mode arisen from the periodic array, the as-designed dielectric nanostructure synchronously manifests excellent spectral features with a bandwidth as narrow as about 2.0 nm, a large Q-factor of 599, perfect transmission amplitude attaining 96% and relatively high electric field intensity (> 2809 times) in the middle of the slotted silicon nanodisk. The as-designed nanostructure possessing these outstanding optical features can work as a high-efficiency refractive-index sensor, whose sensitivity can reach 161.5 nm/RIU with its figure of merit attaining 80.8 RIU−1, efficiently distinguishing an index change of less than 0.01. The proposed slotted silicon nanodisk array exhibits tremendous potential for expanding the application such as label-free biochemical sensing, plasmonic refractive index sensing and surface enhancement spectroscopy.