The traditional minus filter is composed of many layers of thin films, which makes it difficult and complicated to manufacture. It is sensitive to incident light angle and polarization. Here, we propose a near-infrared narrow-band minus filter with a full width at half maximum around 5 nm made of all-dielectric Si-SiO2 structures without any ohmic loss. The stop band transmittance of the proposed filter is close to 0, while its broad pass band transmittance is as high as 90% in the work wavelength range. Theoretical analysis shows that the transmission dip originated from magnetic dipole resonance: Its position can be tuned from 1.3 µm to 1.8 µm by changing the thickness of Si structure, and the proposed structure is insensitive to changes in incident light angle and polarization angle. We further studied its potential applications as a refractive index sensor. The sensitivity of dip1 and dip2 are as high as 953.53 nm/RIU and 691.09 nm/RIU, while their figure of merit is almost unchanged: 59.59 and 115.18, respectively.