Low Earth orbit (LEO) constellations have potentialities to augment global navigation satellite systems for better service performance. The prerequisite is to provide the broadcast ephemerides that meet the accuracy requirement for navigation and positioning. In this study, the Kepler ephemeris model is chosen as the basis of LEO broadcast ephemeris design for backward compatibility and simplicity. To eliminate the singularity caused by the smaller eccentricity of LEO satellites compared to MEO satellites, non-singular elements are introduced for curve fitting of parameters and then transformed to Kepler elements to assure the algorithm of ephemeris computation remains unchanged for the user. We analyze the variation characteristics of LEO orbital elements and establish suitable broadcast ephemeris models considering fit accuracy, number of parameters, fit interval, and orbital altitude. The results of the fit accuracy for different fit intervals and orbital altitudes suggest that the optimal parameter selections are $$(Crs3,Crc3)$$ , $$(Crs3,Crc3, \, \dot{a},\dot{n})$$ and $$\left( {Crs3,Crc3, \, \dot{a},\dot{n}, \, \ddot{i},\ddot{a}} \right)$$ , i.e., adding two, four or six parameters to the GPS 16-parameter ephemeris. When adding four parameters, the fit accuracy can be improved by about one order of magnitude compared to the GPS 16-parameter ephemeris model, and fit errors of less than 10 cm can be achieved with 20-min fit interval for a 400–1400 km orbital altitude. In addition, the effects of the number of parameters, fit interval, and orbit altitude on fit accuracy are discussed in detail. The validation with four LEO satellites in orbit also confirms the effectiveness of proposed models.