To provide a seam welding apparatus and method capable of getting an adequate lap width, which works with a low pressure.

In the seam welding apparatus, a traveling means of clamps for a following sheet has a link mechanism that overlays, at its fully expanded state, the front edge of the following sheet on the rear edge of a proceeding sheet, and a link-driving source to actuate the link mechanism. A pair of link mechanisms are respectively disposed along both side edges of the following sheet, in parallel with them, and the pair of link mechanism are connected to the link-driving source, forming a parallel link mechanism assembled via a connection link. A movable part of a clamping means for the proceeding sheet has a fulcrum for inclined motion that is movably disposed so that the lap width can be adjustable.