As of April 8, 2021, the Danish container shipping company APM-Maersk was operating the most container ships in the world. While having 712 container ships in its fleet, APM-Maersk owned only 298 of them, the rest was either chartered or in its order book. The company’s fleet had a total capacity of roughly 4.1 million twenty-foot equivalent units in 2021.
Source: Statista

