Shape-memory alloys (SMAs) are a rare class of metal compound that after a huge mechanical strain can, on heating, recover their original atomic configuration. In the many useful applications of SMAs, the most studied material is NiTi (nitinol). The understanding on the NiTi properties in nano-scale calculations is still lacking. Here, we present a first-principles density functional theory study of the structural energies, mechanical properties, phase-transformation of NiTi.