Aims. We report on evidence of the inhomogeneity (multiplicity) of the stellar population in the Galactic globular cluster (GC) NGC 3201, which is irregularly reddened across its face. Methods. We carried out a more detailed and careful analysis of our recently published new multi-color photometry in a wide field of the cluster with particular emphasis on the U band. Results. Using the photometric data corrected for differential reddening, we found for the first time two key signs of the inhomogeneity in the cluster's stellar population and of its radial variation in the GC. These are (1) an obvious trend in the color-position diagram, based on the (U − B) color-index, of red giant branch (RGB) stars, which shows that the farther from the cluster's center, the bluer on average the (U − B) color of the stars is; and (2) the dependence of the radial distribution of sub-giant branch (SGB) stars in the cluster on their U magnitude, where brighter stars are less centrally concentrated than their fainter counterparts at a confidence level varying between 99.2% and 99.9% depending on the color-index used to select the stars. The same effects were recently found by us in the GC NGC 1261. However, contrary to NGC 1261, we are not able to unambiguously suggest which of the sub-populations of SGB/RGB stars can be the progenitor of blue and red horizontal branch stars of the cluster. Apart from M4, NGC 3201 is another GC very probably with an inhomogeneous stellar population, which has essentially lower mass than the most massive Galactic GCs where multiple stellar populations were unambiguously detected for the first time.