Recently, Generative Adversarial Networks (GAN)-based methods have shown remarkable performance for the Voice Conversion and WHiSPer-to-normal SPeeCH (WHSP2SPCH) conversion. One of the key challenges in WHSP2SPCH conversion is the prediction of fundamental frequency (F0). Recently, authors have proposed state-of-the-art method Cycle-Consistent Generative Adversarial Networks (CycleGAN) for WHSP2SPCH conversion. The CycleGAN-based method uses two different models, one for Mel Cepstral Coefficients (MCC) mapping, and another for F0 prediction, where F0 is highly dependent on the pre-trained model of MCC mapping. This leads to additional non-linear noise in predicted F0. To suppress this noise, we propose Cycle-in-Cycle GAN (i.e., CinC-GAN). It is specially designed to increase the effectiveness in F0 prediction without losing the accuracy of MCC mapping. We evaluated the proposed method on a non-parallel setting and analyzed on speaker-specific, and gender-specific tasks. The objective and subjective tests show that CinC-GAN significantly outperforms the CycleGAN. In addition, we analyze the CycleGAN and CinC-GAN for unseen speakers and the results show the clear superiority of CinC-GAN.