List-mode positron emission tomography (PET) image reconstruction is an important tool for PET scanners with many lines-of-response (LORs) and additional information such as time-of-flight and depth-of-interaction. Deep learning is one possible solution to enhance the quality of PET image reconstruction. However, the application of deep learning techniques to list-mode PET image reconstruction have not been progressed because list data is a sequence of bit codes and unsuitable for processing by convolutional neural networks (CNN). In this study, we propose a novel list-mode PET image reconstruction method using an unsupervised CNN called deep image prior (DIP) and a framework of alternating direction method of multipliers. The proposed list-mode DIP reconstruction (LM-DIPRecon) method alternatively iterates regularized list-mode dynamic row action maximum likelihood algorithm (LM-DRAMA) and magnetic resonance imaging conditioned DIP (MR-DIP). We evaluated LM-DIPRecon using both simulation and clinical data, and it achieved sharper images and better tradeoff curves between contrast and noise than the LM-DRAMA and MR-DIP. These results indicated that the LM-DIPRecon is useful for quantitative PET imaging with limited events. In addition, as list data has finer temporal information than dynamic sinograms, list-mode deep image prior reconstruction is expected to be useful for 4D PET imaging and motion correction.