This paper focuses on the unsupervised domain adaptation problem for video-based crowd counting, in which we use labeled data as source domain and unlabelled video data as target domain. It is challenging as there is a huge gap between the source and the target domain and no annotations of samples are available in the target domain. The key issue is how to utilize unlabelled videos in the target domain for knowledge learning and transferring from the source domain. To tackle this problem, we propose a novel Error-aware Density Isomorphism REConstruction Network (EDIREC-Net) for cross-domain crowd counting. EDIREC-Net jointly transfers a pre-trained counting model to target domains using a density isomorphism reconstruction objective and models the reconstruction erroneousness by error reasoning. Specifically, as crowd flows in videos are consecutive, the density maps in adjacent frames turn out to be isomorphic. On this basis, we regard the density isomorphism reconstruction error as a self-supervised signal to transfer the pre-trained counting models to different target domains. Moreover, we leverage an estimation-reconstruction consistency to monitor the density reconstruction erroneousness and suppress unreliable density reconstructions during training. Experimental results on four benchmark datasets demonstrate the superiority of the proposed method and ablation studies investigate the efficiency and robustness. The source code is available at https://github.com/GehenHe/EDIREC-Net.