The global characteristics of transient response of a singledegreeoffreedom shape memory oscillator under rectangular pulse excitation were investigated. The equation of motion was established by using a polynomial constitutive model to describe the restitution force of the oscillator. Here, the response of the oscillator under rectangular pulse excitation was divided into two stages. The first stage was the attenuation vibration under an external constant force excitation, while the second stage was the attenuation vibration without any external force excitation. The number of equilibrium points was discussed, and the phase plane and time history of the shape memory oscillator on different conditions were given. Finally, numerical solutions were presented to validate the theoretical results.