Energy finance has grown rapidly and attracted considerable attention for the increasing interactions between energy and financial industries. However, the scope and boundary of energy finance are still unclear due to the diversity of emerging research topics. Therefore, this paper provides a profile of energy finance conducting bibliometric analysis from four dimensions: the intellectual base, research trajectories, intellectual communities, and research fronts. This paper analyzed 10,961 related articles sourced from Web of Science (WOS) since 1904 through three bibliometric analysis approaches: co-citation network analysis, main path analysis and bibliographic coupling analysis. We find that research of energy finance has experienced three stages and can be categorized into five themes: "energy and financial market", "pricing mechanisms of energy", "energy derivative markets", and "green finance". Furthermore, through retrospective and co-citation analyses of the recent literature, we identify six research frontiers: "stock markets and energy prices", "exchange rate and energy market systemic risk modeling", "financial policies related to sustainability and low carbon", "climate and the state of the carbon emissions trading market", "crude oil price forecasting and future market", and "energy infrastructure investment and financing". These findings contribute to the systematic research and an overall mapping of energy finance.