Traditional semi-supervised learning tasks assume that both labeled and unlabeled data follow the same class distribution, but the realistic open-world scenarios are of more complexity with unknown novel classes mixed in the unlabeled set. Therefore, it is of great challenge to not only recognize samples from known classes but also discover the unknown number of novel classes within the unlabeled data. In this paper, we introduce a new open-world semi-supervised novel class discovery approach named OpenNCD, a progressive bi-level contrastive learning method over multiple prototypes. The proposed method is composed of two reciprocally enhanced parts. First, a bi-level contrastive learning method is introduced, which maintains the pair-wise similarity of the prototypes and the prototype group levels for better representation learning. Then, a reliable prototype similarity metric is proposed based on the common representing instances. Prototypes with high similarities will be grouped progressively for known class recognition and novel class discovery. Extensive experiments on three image datasets are conducted and the results show the effectiveness of the proposed method in open-world scenarios, especially with scarce known classes and labels.