The dependency structure contains primary semantic information for interpreting sentences. In conventional approaches for extracting this dependency structure, it is assumed that the complete sentence is known before analysis starts. Therefore, in spontaneous speech, we must detect sentence boundaries. It is necessary for on-line applications to be able to extract the dependency structure from a partial recognition result of a long utterance, but conventional methods are not designed for analyzing such incomplete sentences. In this paper, we propose a sequential dependency analysis method for spontaneous speech. The proposed method enables us to analyze incomplete sentences sequentially and detects sentence boundaries simultaneously. The analyzer can be trained using parsed data based on the maximum entropy principle. Experimental results using spontaneous lecture speech from the CSJ corpus show that our proposed method significantly outperforms a conventional method for analyzing incomplete sentences and achieves nearly the same accuracy for complete sentences.