Some big languages like English are spoken by a lot of people whose mother tongues are different from. Their second languages often have not only distinct accent but also different lexical and syntactic characteristics. Speech recognition performance is severely affected when the lexical, syntactic, or semantic characteristics in the training and recognition tasks differ. Language model of a speech recognition system is usually trained with transcribed speech data or text data collected in English native countries, therefore, speech recognition performance is expected to be degraded by mismatch of lexical and syntactic characteristics between native speakers and second language speakers as well as the distinction between their accents. The aim of language model adaptation is to exploit specific, albeit limited, knowledge about the recognition task to compensate for mismatch of the lexical, syntactic, or semantic characteristics. This paper describes whether the language model adaptation is effective for compensating for the mismatch between the lexical, syntactic, or semantic characteristics of native speakers and second language speakers.