A brain-computer interface (BCI) allows direct communication between the human brain and external devices. Despite impressive performance, previous EEG decoding algorithms still face several challenges: 1) how to shorten or eliminate the calibration process in cross-subject BCI scenarios; 2) how to capture more characteristic features from different scales in EEG data; and 3) how to extract subject-independent EEG features more effectively. To address these problems, we propose a cross-subject EEG decoding algorithm based on a multiscale convolutional neural network (MSCNN) and domain adaptation for P300-based BCIs. The MSCNN was trained on a large-scale EEG dataset to extract subject-independent features. Subsequently, we fine-tune the MSCNN through adversarial discriminative domain adaptation (ADDA) to reduce the differences among cross-subject EEG data. In offline analysis, we achieved a cross-subject average accuracy exceeding 83\%, indicating that we successfully established a cross-subject EEG decoding algorithm, which can eliminate the subject-specific calibration process for new subjects.