The rapid development of minimally invasive surgery technology requires higher flexibility of surgical treatment and small volume of medical instrument. This paper proposed a new type of minimally invasive surgery wrist institution actuated by TiNi shape memory alloy (SMA) wire. The wrist institution has some advantages such as compact structure, flexible function, light weight, big movement space, and high output position precision. The paper briefly introduces the properties of TiNi SMA and describes the configuration of wrist institution. We also carried out mechanism simulation analysis to the mechanics model and set up kinematics equations, and finally presented the workspace of the institution.