Owing to the complex structures of welding materials, special welding conditions, and challenges during the automatic welding of the liquefied natural gas (LNG) ship Mark III’s membrane tank, a series–parallel–series hybrid structure mobile welding robot having sufficient adaptability for welding corrugated plates in membrane tanks was designed in this study. The configuration of the hybrid robot had good workspace characteristics, and it could always maintain a certain distance and angle between the end of the welding torch and the weld line because of its detection and control system coordination. In this study, degrees of freedom, kinematic characteristics, workspace, and adaptability analyses were conducted for the hybrid mechanism. A simulation verification was performed, and a ripple-trajectory-following experiment was conducted using real objects. The simulation and experimental results showed that the welding robot had a reasonable mechanism design, smooth motion, and good terminal distance and angle control, thus meeting the requirements for automatic welding of corrugated plates in membrane tanks.