A Three-DOF (degrees of freedom) parallel mechanism with achievable stable pure translation comprises a base, a moving platform and three structurally identical branches connecting the base and the moving platform. One end of a lower link in each branch is connected with the base through a revolute pair, the other end of this link is connected with one end of an upper link through a lower universal hinge, and the other end of this upper link is connected with the moving platform through an upper universal hinge. Two revolute pairs, connected with the base, of the first and third branches are axially parallel; two upper universal hinge outer revolute pairs, connected with the moving platform, of the first and third branches are axially parallel, the revolute pair, connected with the base, of the second branch is axially perpendicular to the axes of the revolute pairs, connected with the base, of the first and third branches; the upper universal hinge outer revolute pair, connected with the moving platform, of the second branch is axially perpendicular to the axes of the upper universal joint outer revolute pairs, connected with the moving platform, of the first and third branches. The revolute pairs, on different members, of the branches of the mechanism can be naturally parallel, enabling stable three-DOF translational motion without mechanism evolution during moving.