A new family of current-source (CS) mode switched-capacitor (SC) power converters has been proposed in this study, which imposes an alternative solution for power converters especially for CS systems. The conversion ratio of this type converter is analysed and verified here to have one increased degree of freedom using the switching mode and the capacitor-tapping mode, which is a good solution to deal with the limitation of duty cycle adjustment. This research improves the CS mode system that is relatively unexplored in previous works and the proposed work fills the research gap by the sides of the well-established voltage-source (VS) system. An interesting power conversion ratio formulation is obtained, which can produce the wide range of conversion ratio of VS mode switched-inductor power converters and CS mode SC power converters in buck, boost and buck-boost versions. In addition, this proposed CS mode SC power converters have high efficiency of power conversion through simulation and prototype experiments verification. These CS mode converters can flexibly supply power directly to the load powered by the CS and successfully replace the VS mode converters operated under the current environment system.