A new non-overstrained four-DOF parallel kinematic mechanism (PKM) for realizing three-dimensional translations and rotation is presented, which is composed only with revolute joints. The topological structure characteristics, such as the POC set of moving platform, mobility and the mechanism coupling degree, are first obtained based on the design theory of position and orientation characteristic (POC) set. By means of the D—H matrix, the kinematic inverse equations of the PKM are established and Jacobian matrix, singularity are subsequently derived and analyzed. The virtual mechanism is modeled and the kinematics is simulated by using Pro/E software. By comparing the theoretical calculation analysis of examples with the results derived from simulation, the inverse positional solutions are proved to be correct. Based on the kinematic inverse equations, the 3D boundary search method is used to describe the geometrical feature and cross section of constant orientation workspace. Furthermore, the distribution of singularity position is presented and the rotational capacity among the workspace is evaluated. The results show that the workspace has regular geometrical shape and the rotational capacity is satisfactory, but the singular may appear in the workspace. Hence, it is necessary to obtain the singularity-free workspace of the PKM, which can guarantee the mechanism to avoid singularities. The study has guiding significance and reference value to the design and control of this kind of PKM.