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Recurrent neural network transducer (RNN-T) has shown to be comparable with conventional hybrid model for speech recognition. However, there is still a challenge in out-of-domain scenarios with context or words different from training data. In this paper, we explore the semi-supervised training which optimizes RNN-T jointly with neural text-to-speech (TTS) to better generalize to new domains using domain-specific text data. We apply the method to two tasks: one with out-of-domain context and the other with significant out-of-vocabulary (OOV) words. The results show that the proposed method significantly improves the recognition accuracy in both tasks, resulting in 61.4% and 53.8% relative word error rate (WER) reductions respectively, from a well-trained RNN-T with 65 thousand hours of training data. We do further study on the semi-supervised training methodology: 1) which modules of RNN-T model to be updated; 2) the impact of using different neural TTS models; 3) the performance of using text with different relevancy to target domain. Finally, we compare several RNN-T customization methods, and conclude that semi-supervised training with neural TTS is comparable and complementary with Internal Language Model Estimation (ILME) or biasing.