The light-emitting diode (LED)-based light sources have been widely applied across numerous industries and in everyday practical uses. Recently, the LED-based light source consisting of red, green and blue LEDs with narrow spectral bands (RGB-LED) has been a more preferred illumination source than the common white phosphor LED and other traditional broadband light sources because the RGB-LED can create many types of illumination color. The color rendering index of the RGB-LED, however, is considerably lower compared to the traditional broadband light sources and the multi-band LED light source (MB-LED), which is composed of several LEDs and can accurately simulate daylight illuminants. Considering 3 relatively narrow spectral bands of the RGB-LED light source, the color constancy, which is referred to as the ability of the human visual system to attenuate influences of illumination color change and hold the perception of a surface color constant, may be worse under the RGB-LED light source than under the traditional broadband light sources or under the MB-LED. In this study, we investigated categorical color constancy using a color naming method with real Munsell color chips under illumination changes from neutral to red, green, blue, and yellow illuminations. The neutral and 4 chromatic illuminants were produced by the RGB-LED light source. A modified use of the color constancy index, which describes a centroid shift of each color category, was introduced to evaluate the color constancy performance. The results revealed that categorical color constancy under the 4 chromatic illuminants held relatively well, except for the red, brown, orange, and yellow color categories under the blue illumination and the orange color category under the yellow illumination. Furthermore, the categorical color constancy under red and green illuminations was better than the categorical color constancy under blue and yellow illuminations. The results indicate that a color constancy mechanism in the visual system functions in color categories when the illuminant emits an insufficient spectrum to render the colors of reflecting surfaces accurately. However, it is not recommended to use the RGB-LED light source to produce blue and yellow illuminations because of the poor color constancy.