We propose and study Complementary Concept Generation (CCGen): given a concept of interest, e.g., "Digital Cameras", generating a list of complementary concepts, e.g., 1) Camera Lenses 2) Batteries 3) Camera Cases 4) Memory Cards 5) Battery Chargers. CCGen is beneficial for various applications like query suggestion and item recommendation, especially in the e-commerce domain. To solve CCGen, we propose to train language models to generate ranked lists of concepts with a two-step training strategy. We also teach the models to generate explanations by incorporating explanations distilled from large teacher models. Extensive experiments and analysis demonstrate that our model can generate high-quality concepts complementary to the input concept while producing explanations to justify the predictions.