This letter focuses on the cross-corpus speech emotion recognition (SER) task, in which the training and testing speech signals in cross-corpus SER belong to different speech corpora. Existing algorithms are incapable of effectively extracting common sentiment information between different corpora to facilitate knowledge transfer. To address this challenging problem, a novel convolutional auto-encoder and adversarial domain adaptation (CAEADA) framework for cross-corpus SER is proposed. The framework first constructs a one-dimensional convolutional auto-encoder (1D-CAE) for feature processing, which can explore the correlation among adjacent one-dimensional statistic features and the feature representation can be enhanced by the architecture based on encoder-decoder-style. Subsequently the adversarial domain adaptation (ADA) module alleviates the feature distributions discrepancy between the source and target domains by confusing domain discriminator, and specifically employs maximum mean discrepancy (MMD) to better accomplish feature transformation. To evaluate the proposed CAEADA, extensive experiments were conducted on EmoDB, eNTERFACE, and CASIA speech corpora, and the results show that the proposed method outperformed other approaches.