Microstructures play an important role in the research on shape memory alloys (SMA). By using mathematical modeling tools to study microstructures, it is possible to predict the behaviors of these materials under applied fields. In the current paper, a thermo-mechanical model is proposed to simulate the microstructure of a SMA rod with both fixed and impact boundary conditions via Legendre wavelets collocation method. Because of the good performance of Legendre wavelets basis, this method shows excellent properties in both precision and stability. A detailed numerical algorithm is given, and the backward differentiation formula is employed to perform all the simulations in the current paper. Computational simulations are carried out to study the stress-induced phase transformation. The dynamics of microstructure evolution, presented at different temperatures, is well captured by our developed technique.