Abstract: An algebraic elimination method for five precision points path synthesis of spherical four-bar linkage was presented. Firstly, the kinematic constraint equations of path synthesis were formulated based on the displacement matrix; And then, the equations were solved using Groebner-Sylvester (GS) hybrid approach, and a high degree univariate equation and its whole closed-form solutions were accordingly obtained. The results of numerical simulation with Solidworks validate the algorithm, and show that the proposed method can also be used to solve synthesis problems of other kinds of spherical linkages.