Colorimetric detection of target molecules with insensitivity to incident-light polarization has attracted considerable attention in recent years. This resulted from the ability to provide rapid output and reduced assay times as a result of color changes upon altering the environment that are easily distinguishable by the naked eye. In this paper, we propose a highly sensitive refractive-index sensor, utilizing the excitation of guided modes of a novel two-dimensional periodically modulated dielectric grating-waveguide structure. The optimized nanosensor can numerically excite guided-mode resonances with an ultranarrow linewidth (full width at half-maximum) of 0.58 nm. Sensitivity is numerically investigated by considering the deposition of dielectric layers on the structure. For a layer thickness of 30 nm, the maximum sensitivity reached as high as 110 nm/refractive index unit (RIU), resulting in a very high figure of merit of 190. The fabricated devices with 30 nm aluminum oxide and zinc oxide coatings achieved a maximum sensitivity of 235.2 nm/RIU with a linewidth of 19 nm. Colorimetric detection with polarization insensitivity is confirmed practically by a simple optical microscope. Samples with different coatings have been observed to have clearly distinct colors, while the color of each sample is nearly identical upon azimuthal rotation. Excellent agreement is obtained between the numerical and experimental results regarding the spectral position of the resonances and sensitivity. The proposed device is, therefore, highly promising in efficient, highly sensitive, almost lossless, and compact molecular diagnostics in the field of biomedicine with personalized, label-free, early point-of-care diagnosis and field analysis, drug detection, and environmental monitoring.