As electric bicycles (e-bikes) are becoming popular in China, concerns have been raised about their safety conditions. A traffic conflict technique is commonly used in traffic safety analysis, and there are many conflict measures designed for cars. However, e-bikes have high flexibility to change speed and trajectories, which is different from cars, so the conflict measures defined for e-bikes need to be independently explored. Based on e-bike driving characteristics, this paper proposes a new measure, the Integrated Conflict Intensity (ICI), for traffic conflicts involving e-bikes at intersections. It measures the degree of dangerousness of a conflict process, with consideration of both conflict risk and conflict severity. Time to collision is used to measure the conflict risk. Relative kinetic energy is used to measure the conflict severity. ICI can be calculated based on video analysis. The method of determining ICI thresholds for three conflict levels (serious, less serious, and slight) and two conflict types (conflicts between two e-bikes, and conflicts between an e-bike and a car) is put forward based on the questionnaires about safety perception of e-bike riders, which is regarded as the criterion of e-bike safety conditions at intersections. The video recording and a questionnaire survey about conflicts involving e-bikes at intersections have been conducted, and the unified thresholds applicable to different intersections have been determined. It is verified that ICI and its thresholds meet the criterion of e-bike safety conditions. This work is expected to be used in the selection of intersections for safety improvement of e-bike traffic.