This paper presents a noise-robust voice conversion method with high-quefrency boosting via sub-band cepstrum conversion and fusion based on the bidirectional long short-term memory (BLSTM) neural networks that can convert parameters of vocal tracks of a source speaker into those of a target speaker. With the implementation of state-of-the-art machine learning methods, voice conversion has achieved good performance given abundant clean training data. However, the quality and similarity of the converted voice are significantly degraded compared to that of a natural target voice due to various factors, such as limited training data and noisy input speech from the source speaker. To address the problem of noisy input speech, an architecture of voice conversion with statistical filtering and sub-band cepstrum conversion and fusion is introduced. The impact of noises on the converted voice is reduced by the accurate reconstruction of the sub-band cepstrum and the subsequent statistical filtering. By normalizing the mean and variance of the converted cepstrum to those of the target cepstrum in the training phase, a cepstrum filter was constructed to further improve the quality of the converted voice. The experimental results showed that the proposed method significantly improved the naturalness and similarity of the converted voice compared to the baselines, even with the noisy inputs of source speakers.