The invention relates to an apparatus and a method for welding a positioning grid, more particularly to an apparatus and a method for capturing an image of a welding spot during a welding task and determining an accurate position of the welding spot based on the captured image in order to perform an accurate welding task. A laser welding apparatus that the invention is related to comprises: a pulse laser generator, a servo motor, a beam splitter, an imaging sensor and a welding control device. As the constitution of the invention possesses the above properties, the invention captures an image of the welding point when the welding laser position is in a 'closed' state, which is accomplished in parallel to the welding word, thus lessening startup time as required by the welding work and improving working efficiency. In addition, the welding method that the invention is related to provides the captured image in the process of welding work, which can determine the welding state instantly without determination of the welding state after accomplishment of the work, so as to enhance entire working efficiency. The invention, in the meantime, can eradicate image distortion phenomenon resulted from hot spots in the captured image to a maximum extent.