Abstract Cross‐project defect prediction (CPDP) is an important research direction in software defect prediction. Traditional CPDP methods based on hand‐crafted features ignore the semantic information in the source code. Existing CPDP methods based on the deep learning model may not fully consider the differences among projects. Additionally, these methods may not accurately classify the samples near the classification boundary. To solve these problems, the authors propose a model based on multi‐adaptation and nuclear norm (MANN) to deal with samples in projects. The feature of samples were embedded into the multi‐core Hilbert space for distribution and the multi‐kernel maximum mean discrepancy method was utilised to reduce differences among projects. More importantly, the nuclear norm module was constructed, which improved the discriminability and diversity of the target sample by calculating and maximizing the nuclear norm of the target sample in the process of domain adaptation, thus improving the performance of MANN. Finally, extensive experiments were conducted on 11 sizeable open‐source projects. The results indicate that the proposed method exceeds the state of the art under the widely used metrics.