Abstract Part of the long lasting cultural heritage of humanity is the art of classical poems, which are created by fifitting words into certain formats and representations. Automatic poetry composition by computers is considered as a challenging problem which requires high Artifificial Intelligence assistance. This study attracts more and more attention in the research community. In this paper, we formulate the poetry composition task as a natural language generation problem using recurrent neural networks. Given user specifified writing intents, the system generates a poem via sequential language modeling. Unlike the traditional one-pass generation for previous neural network models, poetry composition needs polishing to satisfy certain requirements. Hence, we propose a new generative model with a polishing schema, and output a refifined poem composition. In this way, the poem is generated incrementally and iteratively by refifining each line. We run experiments based on large datasets of 61,960 classic poems in Chinese. A comprehensive evaluation, using perplexity and BLEU measurements as well as human judgments, has demonstrated the effectiveness of our proposed approach