The mobility of a whole parallel manipulator and the relative degree-of-freedom are the key points in mechanism synthesis and analysis, which often can be used to verify the existence of mechanisms. In this paper, the difference between the mobility of a parallel manipulator and the relative degree-of-freedom is discussed. First, a novel relative degree-of-freedom criterion is proposed based on the principle of determining the moving platform by N point positions, which is suitable for a kind of parallel manipulator with spherical joints attached to the moving platform. Next, the relative degree-of-freedom criterion is used to calculate the independent motions of the moving platform compared with the modified Kutzbach–Grübler criterion. The proposed relative degree-of-freedom criterion is different from the modified Kutzbach–Grübler criterion in result value and physical meaning. Finally, the type synthesis of such parallel manipulator with open-loop limbs or closed-loop limbs is performed based on the proposed relative degree-of-freedom criterion.