The concept bottleneck model (CBM) is an interpretable-by-design framework that makes decisions by first predicting a set of interpretable concepts, and then predicting the class label based on the given concepts. Existing CBMs are trained with a fixed set of concepts (concepts are either annotated by the dataset or queried from language models). However, this closed-world assumption is unrealistic in practice, as users may wonder about the role of any desired concept in decision-making after the model is deployed. Inspired by the large success of recent vision-language pre-trained models such as CLIP in zero-shot classification, we propose OpenCBM'' to equip the CBM with open vocabulary concepts via: (1) Aligning the feature space of a trainable image feature extractor with that of a CLIP's image encoder via a prototype based feature alignment; (2) Simultaneously training an image classifier on the downstream dataset; (3) Reconstructing the trained classification head via any set of user-desired textual concepts encoded by CLIP's text encoder. To reveal potentially missing concepts from users, we further propose to iteratively find the closest concept embedding to the residual parameters during the reconstruction until the residual is small enough. To the best of our knowledge, ourOpenCBM'' is the first CBM with concepts of open vocabularies, providing users the unique benefit such as removing, adding, or replacing any desired concept to explain the model's prediction even after a model is trained. Moreover, our model significantly outperforms the previous state-of-the-art CBM by 9% in the classification accuracy on the benchmark dataset CUB-200-2011. The code will be released upon acceptance.