The US$300 million (euro205 million) investment - launched two years ago - is aimed at providing logistic support to Evergreen vessels sailing between China, South Korea and Japan, the Commercial Times quoted unidentified Qingdao Port officials as saying.
It said the dock's unloading and other facilities will be inaugurated soon but did not provide a date.
The investment was made through Hong Kong's Pan Asia Company, it said.
Evergreen, with a fleet of about 100 container vessels, is Taiwan's largest shipping company. Company officials were not available for comment Sunday.
Taiwan strictly regulates investment in infrastructure projects in China. The two sides split amid civil war in 1949.
But Taiwanese companies often bypass the restrictions by investing via their subsidiaries or other overseas firms.