A linear polisher for polishing a substrate that always provides a fresh abrasive surface for polishing and a method for linear polishing a substrate are described. In the linear polisher, a length of a polishing pad is supported on a pair of rollers which are driven by a motor means for either intermittently or continuously advancing the pad during a polishing process. A vibration generator which is connected to the polishing pad through an adaptor provides lateral, or vibration in a transverse direction of the pad throughout the polishing process. The present invention novel linear polisher enables substantially constant removal rate to be achieved throughout the pad life of a polishing pad without deterioration such as that normally seen in a conventional rotary or linear CMP apparatus. Optionally, a rotatable substrate holder is utilized to further improve the polishing uniformity of the linear polishing apparatus.