In this paper, a novel modulation function-based method including analyses of the modulation index and phase is proposed for operation of modular multilevel converters (MMCs) in high voltage direct current (HVDC) transmission systems. The proposed modulation function-based control technique is developed based on thorough and precise analyses of all MMC voltages and currents in the a-b-c reference frame in which the alternating current (AC)-side voltage is the first target to be obtained. Using the AC-side voltage, the combination of the MMC upper and lower arm voltages is achieved as the main structure of the proposed modulation function. The main contribution of this paper is to obtain two very simple new modulation functions to control MMC performance in different operating conditions. The features of the modulation function-based control technique are as follows: (1) this control technique is very simple and can be easily achieved in a-b-c reference frame without the need of using Park transformation; and (2) in addition, the inherent properties of the MMC model are considered in the proposed control technique. Considering these properties leads to constructing a control technique that is robust against MMC parameters changes and also is a very good tracking method for the components of MMC input currents. These features lead to improving the operation of MMC significantly, which can act as a rectifier in the HVDC structure. The simulation studies are conducted through MATLAB/SIMULINK software, and the results obtained verify the effectiveness of the proposed modulation function-based control technique.