Recently, the effectiveness of text-to-speech (TTS) systems combined with neural vocoders to generate high-fidelity speech has been shown. However, collecting the required training data and building these advanced systems from scratch are time and resource consuming. An economical approach is to develop a neural vocoder to enhance the speech generated by existing or low-cost TTS systems. Nonetheless, this approach usually suffers from two issues: 1) temporal mismatches between TTS and natural waveforms and 2) acoustic mismatches between training and testing data. To address these issues, we adopt a cyclic voice conversion (VC) model to generate temporally matched pseudo-VC data for training and acoustically matched enhanced data for testing the neural vocoders. Because of the generality, this framework can be applied to arbitrary TTS systems and neural vocoders. In this paper, we apply the proposed method with a state-of-the-art WaveNet vocoder for two different basic TTS systems, and both objective and subjective experimental results confirm the effectiveness of the proposed framework.