Owing to its unique literal and aesthetical characteristics, automatic generation of Chinese poetry is still challenging in Artificial Intelligence, which can hardly be straightforwardly realized by end-to-end methods. In this paper, we propose a novel iterative polishing framework for highly qualified Chinese poetry generation. In the first stage, an encoder-decoder structure is utilized to generate a poem draft. Afterwards, our proposed Quality-Aware Masked Language Model (QAMLM) is employed to polish the draft towards higher quality in terms of linguistics and literalness. Based on a multi-task learning scheme, QA-MLM is able to determine whether polishing is needed based on the poem draft. Furthermore, QAMLM is able to localize improper characters of the poem draft and substitute with newly predicted ones accordingly. Benefited from the masked language model structure, QAMLM incorporates global context information into the polishing process, which can obtain more appropriate polishing results than the unidirectional sequential decoding. Moreover, the iterative polishing process will be terminated automatically when QA-MLM regards the processed poem as a qualified one. Both human and automatic evaluation have been conducted, and the results demonstrate that our approach is effective to improve the performance of encoder-decoder structure.