Learning accent from crowd-sourced data is a feasible way to achieve a target speaker TTS system that can synthesize accent speech. To this end, there are two challenging problems to be solved. First, direct use of the poor acoustic quality crowd-sourced data and the target speaker data in accent transfer will apparently lead to synthetic speech with degraded quality. To mitigate this problem, we take a bottleneck feature (BN) based TTS approach, in which TTS is decomposed into a Text-to-BN (T2BN) module to learn accent and a BN-to-Mel (BN2Mel) module to learn speaker timbre, where neural network based BN feature serves as the intermediate representation that are robust to noise interference. Second, direct training T2BN using the crowd-sourced data in the two-stage system will produce accent speech of target speaker with poor prosody. This is because the the crowd-sourced recordings are contributed from the ordinary unprofessional speakers. To tackle this problem, we update the two-stage approach to a novel three-stage approach, where T2BN and BN2Mel are trained using the high-quality target speaker data and a new BN-to-BN module is plugged in between the two modules to perform accent transfer. To train the BN2BN module, the parallel unaccented and accented BN features are obtained by a proposed data augmentation procedure. Finally the proposed three-stage approach manages to produce accent speech for the target speaker with good prosody, as the prosody pattern is inherited from the professional target speaker and accent transfer is achieved by the BN2BN module at the same time. The proposed approach, named as AccentSpeech, is validated in a Mandarin TTS accent transfer task.