A modular multilevel converter (MMC) with a conventional centralized control system has many optical fibers for gate signals. A daisy‐chained distributed control system that consists of a primary controller and daisy‐chained cell controllers can reduce the fibers effectively. However, communication delays occur between the controllers and affect the current control performance. This article reveals the current control model of an MMC with phase‐shifted pulse width modulation using the daisy‐chained distributed control system considering the communication delays. We derived a generalized pulse transfer function of the current control and verified it with numerical analyses and circuit simulations. The impacts of the communication delays on the current control and its gain design method are also discussed and analyzed. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.