With the rapid proliferation of online media sources and published news, headlines have become increasingly important for attracting readers to news articles, since users may be overwhelmed with the massive information. In this paper, we generate inspired headlines that preserve the nature of news articles and catch the eye of the reader simultaneously. The task of inspired headline generation can be viewed as a specific form of Headline Generation (HG) task, with the emphasis on creating an attractive headline from a given news article. To generate inspired headlines, we propose a novel framework called POpularity-Reinforced Learning for inspired Headline Generation (PORL-HG). PORL-HG exploits the extractive-abstractive architecture with 1) Popular Topic Attention (PTA) for guiding the extractor to select the attractive sentence from the article and 2) a popularity predictor for guiding the abstractor to rewrite the attractive sentence. Moreover, since the sentence selection of the extractor is not differentiable, techniques of reinforcement learning (RL) are utilized to bridge the gap with rewards obtained from a popularity score predictor. Through quantitative and qualitative experiments, we show that the proposed PORL-HG significantly outperforms the state-of-the-art headline generation models in terms of attractiveness evaluated by both human (71.03%) and the predictor (at least 27.60%), while the faithfulness of PORL-HG is also comparable to the state-of-the-art generation model.