This paper presents a kinematic design of a rotational parallel mechanism, which can perform rotational output motion around two-axes and translational motion of the target point, the center of rotation of the output link. It has an asymmetrical structure and is composed of three connecting chains; one target point control chain with actuators for changing the target point position (TPC), and two rotational motion generating chains having a single input joint in each chain for generating rotational output motion (RMCs). In our previous study, structural synthesis has been carried out and kinematic structures have been clarified in which translational and rotational output motions are fully decoupled, and displacement analysis of one of the structures has been formulated. In the present paper, optimal design of this mechanism was performed taking into consideration actuation and constraint characteristics, and motion range of passive joints in the mechanism. Numerical examples were given to show the effect of the kinematic parameters on the characteristics of the mechanism. Based on the analysis, kinematic parameters have been determined and a prototype mechanism has been designed and built. Experimental results were shown to support the proposed design.