In　this　paper,　a　novel　adaptive　backstepping　nonsingular　fast　terminal　sliding　mode　controller　is　investigated　for　the　chaotic　dynamic　behavior　of　a　third-order　single　machine　infinite　bus　power　system.　The　backstepping　control　strategy　is　employed　to　decompose　the　power　system　model　into　three　subsystems,　and　guarantees　the　progressive　convergence　of　each　subsystem　through　virtual　control.　Meanwhile,　a　novel　nonsingular　fast　terminal　sliding　mode　control　is　designed　to　improve　the　convergence　speed　by　making　the　last　subsystem　converge　in　a　finite　time.　At　the　same　time,　high-order　derivatives　of　state　variables　are　avoided,　and　an　adaptive　rate　is　introduced　to　eliminate　the　interference　of　uncertain　parameters　on　the　system.　The　effectiveness,　robustness　and　superiority　of　the　controller　are　verified　in　simulation　results.　©　2021　IEEE.