In this paper, we investigate the correlation between the radial ultraviolet color distribution and the shapes of the ultraviolet isophote for elliptical galaxies (M32, NGC 1399) and spiral bulges (of M31, M81) by using their archival UIT images. For M31, M81, and NGC 1399, the radial ultraviolet color distributions show a two-component trend; as the distance from the galactic center increase the color becomes redder in the inner region while it becomes bluer in the outer region. On the other hand, the color of M32 continues to become bluer with the increasing galactocentric distance. We also find, unlike the optical/IR images, significant variations of the position angle and the ellipticity in the ultraviolet isophotes of M31, M81, and NGC 1399 through the inner regions. For M32, the variation is significant in the outer region. Since these variation implies the triaxiality of their intrinsic shapes, we suggest that the early-type galaxies and spiral bulges with a radial color gradient in ultraviolet tend to have a triaxiality. On the other hand, the shape parameter characterized by the fourth order cosine Fourier coefficient of the isophote, a(4)/a, indicates that the systematic deviations of the ultraviolet isophotes of the four galaxies are smaller than $~0.2\%$ in units of the semi-major axis. The latter result implies that the ultraviolet isophotes of the galaxies have a pure elliptical shape rather than the boxy or disky shapes. Therefore, there is no clear evidence of correlation between the radial ultra-violet color gradient and the boxy/disky shapes of isophotes.