This　paper　presents　a　method　to　measure　the　piezoelectric　and　elastic　properties　of　the　piezoelectric　wafer　with　sub-surface　damage　by　the　ultrasonic　nondestructive　evaluation.　The　piezoelectric　material　with　sub-surface　damage　is　consider　to　be　a　layered　structure,　which　is　the　homogenous　piezoelectric　material　substrate　covered　with　a　thin　functionally　graded　piezoelectric　material　(FGPM)　film.　For　the　sub-surface　damage　mode,　the　elastic　and　the　electric　parameters　vary　along　the　depth,　while　the　density　of　FGMP　is　constant.　Both　the　linear　and　exponential　damage　profile　are　studied　in　the　numerical　example.　Influences　of　profile　of　the　damage　along　the　depth　and　the　thickness　of　the　sub-surface　damage　region　on　the　surface　wave＇s　dispersion　relations　are　discussed.　By　the　relationship　of　the　changing　value　of　phase　velocities　and　the　frequency　of　the　surface　waves,　the　profile　of　the　sub-surface　damage　of　the　piezoelectric　wafer　can　be　described　by　experimental　measurement.