An oxygen-compression apparatus has a driving device, multiple rotating wheels, multiple driving rings, multiple rocking cylinders and multiple connecting hoses. The driving device has a driving shaft with a central axis. The rotating wheels are eccentrically attached on and rotated with the driving shaft and are located respectively at different angles relative to the central axis of the driving shaft. The driving rings are rotatably mounted respectively around the rotating wheels. The rocking cylinders are connected respectively to the driving rings and each has a housing and a piston rod. The piston rod has a first end extending into the inner space of the housing to form a compression chamber in the inner space and a second end pivotally connected to a corresponding one of the driving rings. The connecting hoses are connected between the compression chambers of adjacent rocking cylinders.