Composite workpieces, especially the complex-curved surfaces composite workpieces, have been increasingly used in different industries. Non-destructive testing of these parts has become an urgent problem to be addressed. To solve the problem, this article presents a dual-robot air-coupled ultrasonic non-destructive testing scheme and introduces the structure of the system and a general calibration method for the workpiece frame of a dual-robot system in detail. Importantly, this article proposes a tangential constraint method, which makes the probes completely aligned during the inspection process. Verification experiments and ultrasonic testing experiments for a glued multilayered composite workpiece were performed using the dual-robot air-coupled ultrasonic non-destructive testing system. A comparative experiment was also performed using a dual-robot water jet-coupling ultrasonic testing system. Experimental results show that the dual-robot non-destructive testing scheme and the tangential constraint method function well, and all the artificial defects on the sample can be detected by both kinds of testing methods. Vivid 3-D C-scan image based on the test result is provided for convenience of observation. In other words, a kind of flexible versatile testing platform with multiple degrees of freedom is established.