Immunoglobulins are crucial proteins produced by the immune system to identify and bind to foreign substances, playing an essential role in shielding organisms from infections and diseases. Designing specific antibodies opens new pathways for disease treatment. With the rise of deep learning, AI-driven drug design has become possible, leading to several methods for antibody design. However, many of these approaches require additional conditions that differ from real-world scenarios, making it challenging to incorporate them into existing antibody design processes. Here, we introduce IgGM, a generative model for the de novo design of immunoglobulins with functional specificity. IgGM simultaneously generates antibody sequences and structures for a given antigen, consisting of three core components: a pre-trained language model for extracting sequence features, a feature learning module for identifying pertinent features, and a prediction module that outputs designed antibody sequences and the predicted complete antibody-antigen complex structure. IgGM effectively predicts structures and designs novel antibodies and nanobodies. This makes it highly applicable in a wide range of practical situations related to antibody and nanobody design. Code is available at: https://github.com/TencentAI4S/IgGM.