In the present paper the basic characteristics (length, peak intensity, and full-width half-maximum) of nanojets formed in the vicinity of dielectric core-shell cuboids with different types of index grading are investigated by finite-difference time domain method. The latitudinal and longitudinal sizes of a nanojet and its peak intensity depending on the optical contrast variation of cuboids core-shells are numerically investigated. It has been shown that it is possible to control and elongate the nanojet abnormally. It also was shown that graded cuboid with dimensions of 4 × 4 × 4 wavelength may has FWHM of a jet less than uniform cuboid with dimensions of 1 × 1 × 1 wavelength. At wavelength of 600 nm graded index cuboid with dimensions of 4 × 4 × 4 wavelength and index grading = 2 allow to form photonic jet with FWHM about 232 nm or 0.39 wavelength.