The atmospheric energy budget is often adopted by previous studies to explore the balance between energy sources/sinks and the divergence of atmospheric energy flux. Because the atmospheric circulation is essentially generated by the energy balance between sources and sinks, a better knowledge of an energy budget will lead to a better understanding of the atmospheric circulation and its variations.;Climatologically, the polar regions are the major sink regions of global energy. The energy in the polar regions undergoes interannual and 30-60 day variations. It was inferred from previous studies dealing with the poleward propagation of angular momentum that energy exhibits a propagating signature, originating from the tropics and extending into the polar regions, on the interannual and 30-60 day timescales. To gain a new perspective on the polar energy change, the polar energy budget was studied in this thesis, based on a hypothesis that the low-latitude atmospheric energy with poleward propagation could indirectly affect the divergence of energy flux, and, in turn, affect the variations of the polar energy budget. In addition, polar climate changes (e.g., precipitation) associated with the energy propagation were also studied.;Results indicated that the energy changes in the polar regions and the tropics are remotely linked through the poleward propagation of energy relay carried out by different types of circulation patterns at different latitudes, as the propagation of angular momentum depicted by previous studies. Analyses have pointed out that the propagation of energy is led by the divergence of energy flux with a horizontal quadrature shift between the former and the latter. After a larger (smaller) energy propagates into the polar regions, the polar energy budget is changed by an increase (decrease) of energy transport into the polar regions. On the other hand, it was found that the increase (decrease) of energy flux converging into the polar regions is balanced by an increase (decrease) of downward surface flux and upward radiation flux at the top of the atmosphere over the polar regions. Associated with this energy balance, the polar climate changes include a reduced (increased) precipitation and an increased (reduced) outgoing longwave radiation. Maintenance of these changes were discussed.