As a new geometric representation and calculation system, the conformal geometric algebra has been recognized as a research hotspot in recent years. But as a new branch of algebra, the conformal geometric algebra is still in the process of development, especially its application in theory of mechanism is relatively deficient at present. The new geometric algebra method for the kinematics analysis of spatial parallel mechanisms was studied and a conformal geometric algebra method integrating geometric representation and calculation was proposed. With the origin of coordinates on the moving platform describing its position and Euler angles describing its orientation, the conformal geometric algebra expression of an arbitrary point’s location on the moving platform in the fixed coordinate system was presented. Then a method to establish kinematics equations for the kinematics analysis of spatial parallel mechanisms was proposed to conduct the forward and inverse kinematics analysis of spatial parallel mechanisms. A 4-UPU parallel mechanism was taken as an example to illustrate the proposed conformal geometric algebra method for kinematics analysis of spatial parallel mechanisms. And a numerical example was given to verify correctness and effectiveness of the proposed approach. The proposed conformal geometric algebra method was a new method for the kinematics analysis of spatial parallel mechanisms by integrating geometric representation and computation.