Monocular depth estimation is one of the fundamental tasks in environmental perception and has achieved tremendous progress in virtue of deep learning. However, the performance of trained models tends to degrade or deteriorate when employed on other new datasets due to the gap between different datasets. Though some methods utilize domain adaptation technologies to jointly train different domains and narrow the gap between them, the trained models cannot generalize to new domains that are not involved in training. To boost the transferability of depth estimation models, we propose an adversarial depth estimation task and train the model in the pipeline of meta-learning. Our proposed adversarial task mitigates the issue of meta-overfitting, since the network is trained in an adversarial manner and aims to extract domain invariant representations. In addition, we propose a constraint to impose upon cross-task depth consistency to compel the depth estimation to be identical in different adversarial tasks, which improves the performance of our method and smoothens the training process. Experiments demonstrate that our method adapts well to new datasets after few training steps during the test procedure.