Accurate channel state information (CSI) feedback plays a vital role in improving the performance gain of massive multiple-input multiple-output (m-MIMO) systems, where the dilemma is excessive CSI overhead versus limited feedback bandwith. By considering the noisy CSI due to imperfect channel estimation, we propose a novel deep neural network architecture, namely AnciNet, to conduct the CSI feedback with limited bandwidth. AnciNet extracts noise-free features from the noisy CSI samples to achieve effective CSI compression for the feedback. Experimental results verify that the proposed AnciNet approach outperforms the existing techniques under various conditions.