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To mitigate the adverse structural responses, an improved version of the traditional tuned vibration absorber has been proposed based on the shape memory alloy spring, referred as the shape memory alloy-spring tuned vibration absorber. The finite element numerical models of the multi-degree-of-freedom structure (e.g., transmission tower) and shape memory alloy-spring tuned vibration absorber are developed by using the commercial software ANSYS, and the nonlinear behavior of the shape memory alloy spring is validated based on a previous experimental study. The damping mechanism of the shape memory alloy-spring tuned vibration absorber attached to a multi-degree-of-freedom structure under seismic excitations is investigated, and the nonlinear hysteretic behavior of the shape memory alloy spring is also discussed. The results show that the proposed damper has a two-stage damping mechanism, and its control performance is remarkable. Because the coupled system response is sensitive to the amplitude level, the optimal configuration of the shape memory alloy-spring tuned vibration absorber can be obtained by parametric analysis. Particularly, because of the nonlinear target energy transfer and transient resonance capture mechanism, the shape memory alloy-spring tuned vibration absorber exhibits stable control ability under different seismic waves, indicating a good stability in vibration control of a multi-degree-of-freedom system. [ABSTRACT FROM AUTHOR]