The full-field pulse-echo ultrasonic propagation imaging (PE UPI) system using a two-axis linear stage has been successfully used to perform a non-destructive evaluation of flat specimens. This study used a six-axis robot arm to develop a robotic scanning algorithm that can be applied to the laser pulse-echo inspection of non-flat objects. The robotic PE UPI system was constructed and verified for both flat and curved specimens. The internal structures and defects of a honeycomb sandwich plate and a glass-fibre-reinforced polymer specimen were visualised by the robotic PE UPI system. The quality of the evaluation of the flat specimen was equivalent to that of a two-axis linear system, and the result of the curved specimen showed improvement compared to that of the linear system. The ability of the robotic scanning technique to evaluate the structural health performance of arbitrarily shaped surfaces was validated.