The graded thermal conductivity in nanoscale “hot spot” system is a new phenomenon in nanoscale heat conduction. It is found that the thermal conductivity is no longer uniform, and the thermal conductivity gradually increases from the inside to the outside in the radial direction, which no longer obeys Fourier’s law of thermal conductivity. An in-depth understanding of the mechanism of the graded thermal conductivity can provide a theoretical basis for solving engineering problems such as heat dissipation of nanochip. This paper first reviews the new phenomenon of heat conduction recently discovered in nanosystem, then, focuses on the graded thermal conductivity in the “hot spot” system, and expounds the variation law of the graded thermal conductivity in different dimensional systems. According to the changes of atomic vibration mode and phonon scattering, the physical mechanism of the graded thermal conductivity is explained. Finally, the new challenges and opportunities brought by the graded thermal conductivity characteristics of nano “hot spot” to the heat dissipation of nanodevices are summarized, and the future research in this direction is also prospected.