Automatically generating Conceptual Graphs (CGs) [1] from natural language sentences is a difficult task in using CG as a semantic (knowledge) representation language for natural language information source. However, up to now only few approaches have been proposed for this task and most of them either are highly dependent on one domain or use manual rules. In this paper, we propose a machine-learning based approach that can be trained for different domains and requires almost no manual rules. We adopt a dependency grammar-Link Grammar [2] - for this purpose. The link structures of the grammar are very similar to conceptual graphs. Based on the link structure, through the word-conceptualization, concept-folding, link-folding and relationalization operations, we can train the system to generate conceptual graphs from domain specific sentences. An implementation system of the method is currently under development with IBM China Research Lab.