The work aims to design a multi-axis synchronous control algorithm by deviation coupling control, in order to improve the accuracy of multi-axis synchronous control in corrugated carton printing process. Based on the introduction to the structure of corrugated printing machine and with multi-motor control of printing module as the research object, the multi-axis position control was expounded based on the deviation coupling control. In order to reduce the synchronous error, a variable-domain fuzzy control algorithm was designed. On the basis of traditional fuzzy control, flex factor was introduced to realize dynamic adjustment of input and output of fuzzy control. A multi-axis synchronous controller was designed based on ARM and FPGA. Finally, an experimental study was carried out. The synchronous error of the motor tended to 0 within 1 s, and the synchronous performance was ideal. The variable-domain fuzzy control method could control the maximum synchronous position error within 2 rad/s. The accuracy of color overprinting was relatively high, and there were no misprints. The corrugated carton multi-axis control method has a relatively fast response speed and stable operation, which can fully meet the requirements of corrugated carton printing.