Recently, event-based stereo matching has been studied due to its robustness in poor light conditions. However, existing event-based stereo networks suffer severe performance degradation when domains shift. Unsupervised domain adaptation (UDA) aims at resolving this problem without using the target domain ground-truth. However, traditional UDA still needs the input event data with ground-truth in the source domain, which is more challenging and costly to obtain than image data. To tackle this issue, we propose a novel unsupervised domain Adaptive Dense Event Stereo (ADES), which resolves gaps between the different domains and input modalities. The proposed ADES framework adapts event-based stereo networks from abundant image datasets with ground-truth on the source domain to event datasets without ground-truth on the target domain, which is a more practical setup. First, we propose a self-supervision module that trains the network on the target domain through image reconstruction, while an artifact prediction network trained on the source domain assists in removing intermittent artifacts in the reconstructed image. Secondly, we utilize the feature-level normalization scheme to align the extracted features along the epipolar line. Finally, we present the motion-invariant consistency module to impose the consistent output between the perturbed motion. Our experiments demonstrate that our approach achieves remarkable results in the adaptation ability of event-based stereo matching from the image domain.