Recently automatic speech recognition (ASR) systems achieve higher and higher accuracy rates. However, the score drops significantly, when the ASR system is being used with a non-native speaker of the language to be recognized, mainly because of specific pronunciation and accent features. A limited volume of labeled datasets containing samples of a non-native speech makes it difficult to train any new ASR systems targeted for non-native speakers. In our research, we tried tackling the problem of a non-native accent and its influence on the accuracy of ASR systems, using the style transfer methodology. We designed a pipeline for modifying the speech produced by a nonnative speaker, so that it resembles the native speech to a higher extent, i.e. a method for accent neutralization. Our methodology can be used as a wrapper for any existing ASR system, which reduces the necessity of training new speech recognizers, adapted for non-native speech. The modification can be thus performed on the fly, before passing the data forward to the speech recognition system itself.