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Understanding the origins of small-scale flats of CCDs and their wavelength-dependent variations plays an important role in high-precision photometric, astrometric, and shape measurements of astronomical objects. Based on the unique flat data of 47 narrowband filters provided by JPAS-Pathfinder, we analyze the variations of small-scale flats as a function of wavelength. We find moderate variations (from about 1.0% at 390 nm to 0.3% at 890 nm) of small-scale flats among different filters, increasing toward shorter wavelengths. Small-scale flats of two filters close in central wavelengths are strongly correlated. We then use a simple physical model to reproduce the observed variations to a precision of about ±0.14% by considering the variations of charge collection efficiencies, effective areas, and thicknesses between CCD pixels. We find that the wavelength-dependent variations of the small-scale flats of the JPAS-Pathfinder camera originate from inhomogeneities of the quantum efficiency (particularly charge collection efficiency), as well as the effective area and thickness of CCD pixels. The former dominates the variations in short wavelengths, while the latter two dominate at longer wavelengths. The effects on proper flat-fielding, as well as on photometric/flux calibrations for photometric/slitless spectroscopic surveys, are discussed, particularly in blue filters/wavelengths. We also find that different model parameters are sensitive to flats of different wavelengths, depending on the relations between the electron absorption depth, photon absorption length, and CCD thickness. In order to model the wavelength-dependent variations of small-scale flats, a small number (around 10) of small-scale flats with well-selected wavelengths are sufficient to reconstruct small-scale flats in other wavelengths. © 2021. The American Astronomical Society. All rights reserved.