This paper proposes a 3D geometric constraint solving method, based on equivalence analysis in graph theory, that can handle over-constrained, well-constrained, and under-constrained configurations naturally and efficiently. The basic idea is that there are equivalent geometric constraint systems with different geometric constraint graphs. If the geometric domain knowledge is exploited to transform a geometric constraint system into an equivalent one that has a better geometric constraint graph structure using equivalent constraint substitution, the decomposition of geometric constraint system can be optimized. Therefore, the proposed approach will not depend on the initial geometric constraint graph structure, but on the inherent characteristic of the geometric constraint system. This proposition can usually find the optimal decomposition of the geometric constraint system. Several typical examples have been given to illustrate the correctness and effectiveness of the proposed method.