Deep learning-based object counting models have recently been considered preferable choices for plant counting. However, the performance of these data-driven methods would probably deteriorate when a discrepancy exists between the training and testing data. Such a discrepancy is also known as the domain gap. One way to mitigate the performance drop is to use unlabeled data sampled from the testing environment to correct the model behavior. This problem setting is also called unsupervised domain adaptation (UDA). Despite UDA has been a long-standing topic in machine learning society, UDA methods are less studied for plant counting. In this paper, we first evaluate some frequently-used UDA methods on the plant counting task, including feature-level and image-level methods. By analyzing the failure patterns of these methods, we propose a novel background-aware domain adaptation (BADA) module to address the drawbacks. We show that BADA can easily fit into object counting models to improve the cross-domain plant counting performance, especially on background areas. Benefiting from learning where to count, background counting errors are reduced. We also show that BADA can work with adversarial training strategies to further enhance the robustness of counting models against the domain gap. We evaluated our method on 7 different domain adaptation settings, including different camera views, cultivars, locations, and image acquisition devices. Results demonstrate that our method achieved the lowest Mean Absolute Error on 6 out of the 7 settings. The usefulness of BADA is also supported by controlled ablation studies and visualizations.