The invention discloses a two-freedom-degree parallel-connection rotation mechanism with a spherical surface pure-rolling property. The mechanism comprises a fixed base, a motion platform and branch kinematic chains, wherein the branch kinematic chains further includes two different types of branch kinematic chains, different numbers and types of branch kinematic chains, fixed bases and motion platforms can form twelve types of two-freedom-degree parallel-connection rotation mechanisms with the spherical surface pure-rolling property, each mechanism can achieve that the motion platform carries out two-freedom-degree equal-diameter spherical surface pure-rolling rotation around the fixed base, and the relative positions of all the branch kinematic chains of each parallel-connection mechanism can be asymmetrically arranged according to specific using requirements. The two-freedom-degree parallel-connection rotation mechanism with the spherical surface pure-rolling property has the advantages of being large in rigidity, strong in bearing capacity and multiple in structure type, each structure can achieve the two-freedom-degree equal-diameter spherical surface pure-rolling rotation, only rotation pairs are contained in the mechanism, the two-freedom-degree parallel-connection rotation mechanism is simple in structure and easy to manufacture, and accessories such as sensors can be installed conveniently.