Connecting legs of modular multilevel converters (MMCs) in parallel can assist an MMC-based high-voltage direct current (HVDC) to increase its current ratings and hence overall power handling capability. Consequently, each phase of the MMC would be integrated by several legs or sets of upper and lower arms (ULAs). This paper proposes a current control strategy for each ULA in order to ensure balanced current sharing among them. In addition, each ULA has its own circulating current control that follows a reference obtained from the instantaneous magnitudes of the output current and the modulation signal. All the proposed control actuations do not distort the phase output voltage of the MMC which follows the reference voltage. The performance of the proposed control strategies is evaluated by simulation studies in the PLECS Blockset under MATLAB/Simulink software platform.