Objective. Many subject-dependent methods were proposed for electroencephalogram (EEG) classification in rapid serial visual presentation (RSVP) task, which required a large amount of data from new subject and were time-consuming to calibrate system. Cross-subject classification can realize calibration reduction or zero calibration. However, cross-subject classification in RSVP task is still a challenge. Approach. This study proposed a multi-source domain adaptation based tempo-spatial convolution (MDA-TSC) network for cross-subject RSVP classification. The proposed network consisted of three modules. First, the common feature extraction with multi-scale tempo-spatial convolution was constructed to extract domain-invariant features across all subjects, which could improve generalization of the network. Second, the multi-branch domain-specific feature extraction and alignment was conducted to extract and align domain-specific feature distributions of source and target domains in pairs, which could consider feature distribution differences among source domains. Third, the domain-specific classifier was exploited to optimize the network through loss functions and obtain prediction for the target domain. Main results. The proposed network was evaluated on the benchmark RSVP dataset, and the cross-subject classification results showed that the proposed MDA-TSC network outperformed the reference methods. Moreover, the effectiveness of the MDA-TSC network was verified through both ablation studies and visualization. Significance. The proposed network could effectively improve cross-subject classification performance in RSVP task, and was helpful to reduce system calibration time.