Plasmonic nanoantenna arrays have been investigated in connection with spectral filtering applications in the last decade. We show that an all-dielectric nanoantenna can also perform a similar function. We propose a nanocross-shaped nanoantenna array design and present a numerical study of spectral filters based on this design. A broad gamut of colors is achievable in both the reflective and transmissive modes and is reasonably robust to fabrication-related imperfections. These all-dielectric ultrathin spectral filters are promising for the realization of multispectral image sensors and low-power displays.