Nowadays automatic speech recognition (ASR) systems can achieve higher and higher accuracy rates depending on the methodology applied and datasets used. The rate decreases significantly when the ASR system is being used with a non-native speaker of the language to be recognized. The main reason for this is specific pronunciation and accent features related to the mother tongue of that speaker, which influence the pronunciation. At the same time, an extremely limited volume of labeled non-native speech datasets makes it difficult to train, from the ground up, sufficiently accurate ASR systems for non-native speakers. In this research we address the problem and its influence on the accuracy of ASR systems, using the style transfer methodology. We designed a pipeline for modifying the speech of a non-native speaker so that it more closely resembles the native speech. This paper covers experiments for accent modification using different setups and different approaches, including neural style transfer and autoencoder. The experiments were conducted on English language pronounced by Japanese speakers (UME-ERJ dataset). The results show that there is a significant relative improvement in terms of the speech recognition accuracy. Our methodology reduces the necessity of training new algorithms for non-native speech (thus overcoming the obstacle related to the data scarcity) and can be used as a wrapper for any existing ASR system. The modification can be performed in real time, before a sample is passed into the speech recognition system itself.