A Fundamental Frequency Sorting Algorithm (FFSA) is proposed in this paper to balance the voltages of floating dc capacitors for Modular Multilevel Converters (MMCs). The main idea is to change the sequences of the CPS-PWM carriers according to the capacitor voltage increments during the previous fundamental period. Excessive frequent sorting is avoided and many calculating resources are saved for the controller. As a result, more sub-modules can be dealt with. Furthermore, it does not need to measure the arm currents. Therefore, the communication between the controllers can be simplified and the number of current sensors can be reduced. Moreover, the proposed balancing method guarantees that all of the switching frequencies of the sub-modules are equal to each other. This is quite beneficial for the thermal design of the sub-modules and the lifetime of the power switches. Simulation and experimental results acquired from a 9-level prototype verify the viability of the proposed balancing method.