This paper presents a robust model for language understanding in spoken dialogue systems, in which the understanding problem is formulated as a three-stage process. In the first stage, semantic concepts included in the utterance are identified through a bottom-up chart parser to build a concept graph. Then, in the second stage, communicative goal of each candidate path searched from the concept graph is determined by a classifier based on latent semantic analysis. Finally, information of discourse history is introduced to guide the search in all hypotheses for the best result. Experiments with a test set composed of spontaneous utterances show that this model outperforms a rule-based model by 8.1% and 21.5% in goal and concept understanding respectively, which proves its advantage to robust spontaneous language understanding.