Click-through rate (CTR) prediction plays important role in personalized advertising and recommender systems. Though many models have been proposed such as FM, FFM and DeepFM in recent years, feature engineering is still a very important way to improve the model performance in many applications because using raw features can rarely lead to optimal results. For example, the continuous features are usually transformed to the power forms by adding a new feature to allow it to easily form non-linear functions of the feature. However, this kind of feature engineering heavily relies on peoples experience and it is both time consuming and labor consuming. On the other side, concise CTR model with both fast online serving speed and good model performance is critical for many real life applications. In this paper, we propose LeafFM model based on FM to generate new features from the original feature embedding by learning the transformation functions automatically. We also design three concrete Leaf-FM models according to the different strategies of combing the original and the generated features. Extensive experiments are conducted on three real-world datasets and the results show Leaf-FM model outperforms standard FMs by a large margin. Compared with FFMs, Leaf-FM can achieve significantly better performance with much less parameters. In Avazu and Malware dataset, add version Leaf-FM achieves comparable performance with some deep learning based models such as DNN and AutoInt. As an improved FM model, Leaf-FM has the same computation complexity with FM in online serving phase and it means Leaf-FM is applicable in many industry applications because of its better performance and high computation efficiency.