Abstract: Proposed a modeling approach using conformal geometric algebra and an improved Sylvester resultant elimination method for forward displacement analysis of a planar parallel mechanism. Based on representation of points in five-dimensional conformal space containing unknown parameters, the modeling approach using conformal geometric algebra for forward displacement analysis was presented. An improved Sylvester resultant elimination method was proposed, namely redundant factor elimination method. A six-degree equation with one unknown was derived by the proposed method to obtain correct roots. A numerical example of the parallel mechanism with six groups of solutions of positions and postures without extraneous roots or missing roots verifies that the proposed method is correct and effective.