In order to adopt feature-based parametric modeling, CAD/CAM applications must have a geometric constraint solver that can handle a large set of geometric configurations efficiently and robustly. In this paper, we describe a graph constructive approach to solving geometric constraint problems. Usually, a graph constructive approach is efficient, however it has its limitation in scope; it cannot handle ruler-and-compass non-constructible configurations and under-constrained problems. To overcome these limitations. we propose an algorithm that isolates ruler-and-compass non-constructible configurations from ruler-and-compass constructible configurations and applies numerical calculation methods to solve them separately. This separation can maximize the efficiency and robustness of a geometric constraint solver. Moreover, the solver can handle under-constrained problems by classifying under-constrained subgraphs to simplified cases by applying classification rules. Then, it decides the calculating sequence of geometric entities in each classified case and calculates geometric entities by adding appropriate assumptions or constraints. By extending the clustering types and defining several rules, the proposed approach can overcome limitations of previous graph constructive approaches which makes it possible to develop an efficient and robust geometric constraint solver.