In product description generation (PDG), the user-cared aspect is critical for the recommendation system, which can not only improve user's experiences but also obtain more clicks. High-quality customer reviews can be considered as an ideal source to mine user-cared aspects. However, in reality, a large number of new products (known as long-tailed commodities) cannot gather sufficient amount of customer reviews, which brings a big challenge in the product description generation task. Existing works tend to generate the product description solely based on item information, i.e., product attributes or title words, which leads to tedious contents and cannot attract customers effectively. To tackle this problem, we propose an adaptive posterior network based on Transformer architecture that can utilize user-cared information from customer reviews. Specifically, we first extend the self-attentive Transformer encoder to encode product titles and attributes. Then, we apply an adaptive posterior distillation module to utilize useful review information, which integrates user-cared aspects to the generation process. Finally, we apply a Transformer-based decoding phase with copy mechanism to automatically generate the product description. Besides, we also collect a large-scare Chinese product description dataset to support our work and further research in this field. Experimental results show that our model is superior to traditional generative models in both automatic indicators and human evaluation.