The　propagation　behavior　of　Love　waves　in　a　functionally　graded　material　layered　non-piezoelectric　half-space　with　initial　stress　is　taken　into　account.　The　Wentzel-Kramers-Brillouin　(WKB)　technique　is　adopted　for　the　theoretical　derivations.　The　analytical　solutions　are　obtained　for　the　dispersion　relations　and　the　distributions　of　the　mechanical　displacement　and　stress　along　the　thickness　direction　in　the　layered　structure.　First,　these　solutions　are　used　to　study　the　effects　of　the　initial　stress　on　the　dispersion　relations　and　the　group　and　phase　velocities,　then　the　influences　of　the　initial　stress　on　the　distributions　of　the　mechanical　displacement　and　shear　stresses　along　the　thickness　direction　are　discussed　in　detail.　Numerical　results　obtained　indicate　that　the　phase　velocity　of　the　Love　waves　increases　with　the　increase　in　the　magnitude　of　the　initial　tensile　stress,　while　decreases　with　the　increase　in　the　magnitude　of　the　initial　compression　stress.　The　effects　on　the　dispersion　relations　of　the　Love　wave　propagation　are　negligible　as　the　magnitudes　of　the　initial　stress　are　less　than　100　MPa.　Some　other　results　are　obtained　for　the　distributions　of　field　quantities　along　thickness　direction.　The　results　obtained　are　not　only　meaningful　for　the　design　of　functionally　graded　structures　with　high　performance　but　also　effective　for　the　evaluation　of　residual　stress　distribution　in　the　layered　structures.　(C)　2008　Elsevier　Ltd.　All　rights　reserved.