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Speech interfaces using LVCSR system have promise for improving the utility of Open-domain Question Answering, in which natural language questions about diversified topics are used as inputs. In this paper, we propose a method to improve both speech recognition and question answering performance by incorporating the passage retrieval, which is a component common to many QA systems, with respect to the target documents that the input question asked about. In the QA process, the passage that has the high similarity to the question has the high possibility to have the correct answer in it. Conversely, this similarity can be used to select the appropriate candidate from N-best list of speech recognition results. From language modeling perspective, this process can be seen to capture the semantic consistency of spoken question in sentence level as compared with conventional n-gram language models. We show the effectiveness of our method by means of experiments.