This paper conducts a parametric study of a new tuned mass damper with pre-strained superelastic SMA helical springs (SMAS-TMD) on the vibration reduction effect. First, a force-displacement relation model of superelastic SMA helical spring is presented based on the multilinear constitutive model of SMA material, and the tension tests of the six SMA springs fabricated are implemented to validate the mechanical model. Then, a dynamic model of a single floor steel frame with the SMAS-TMD damper is set up to simulate the seismic responses of the frame, which are testified by the shaking table tests. The wire diameter, initial coil diameter, number of coils and pre-strain length of SMA springs are extracted to investigate their influences on the seismic response reduction of the frame. The numerical and experimental results show that, under different earthquakes, when the wire diameter, initial coil diameter and number of coils are set to the appropriate values so that the initial elastic stiffness of the SMA spring is between 0.37 and 0.58 times of classic TMD stiffness, the maximum reduction ratios of the proposed damper can reach 40% as the mass ratio is 2.34%. Meanwhile, when the pre-strain length of SMA spring is in a suitable range, the SMAS-TMD damper can also achieve very good vibration reduction performance. The vibration reduction performance of the SMAS-TMD damper is generally equal to or better than that of the classic optimal TMD, and the proposed damper effectively suppresses the detuning phenomena that often occurs in the classic TMD.