Modern industrial fault diagnosis tasks often face the combined challenge of distribution discrepancy and bi-imbalance. Existing domain adaptation approaches pay little attention to the prevailing bi-imbalance, leading to poor domain adaptation performance or even negative transfer. In this work, we propose a self-degraded contrastive domain adaptation (Sd-CDA) diagnosis framework to handle the domain discrepancy under the bi-imbalanced data. It first pre-trains the feature extractor via imbalance-aware contrastive learning based on model pruning to learn the feature representation efficiently in a self-supervised manner. Then it forces the samples away from the domain boundary based on supervised contrastive domain adversarial learning (SupCon-DA) and ensures the features generated by the feature extractor are discriminative enough. Furthermore, we propose the pruned contrastive domain adversarial learning (PSupCon-DA) to pay automatically re-weighted attention to the minorities to enhance the performance towards bi-imbalanced data. We show the superiority of the proposed method via two experiments.