A laser processing apparatus includes a laser oscillator configured to oscillate a laser beam, a first condenser configured to focus an S-polarized laser beam, a second condenser configured to focus a P-polarized laser beam, an X-moving unit configured to processing-feed a holding table that holds a wafer thereon in X directions, and first and second indexing feed units configured to indexing-feed the first and second condensers respectively in Y directions. While the wafer is being processed with the laser beam from the first condenser along a projected dicing line on the wafer in the X directions, the second condenser is indexing-fed and positioned on a next projected dicing line along which to process the wafer.