The　stress　at　the　boundary　of　adjacent　layers　is　discontinuous　when　the　conventional　Laguerre　orthogonal　polynomial　method　is　used　to　calculate　the　propagation　characteristics　of　Rayleigh-like　waves　on　a　layered　semi-infinite　structure.　This　problem　results　in　an　error　of　wave　velocity　calculation,　primarily　when　the　mechanical　properties　of　the　adjacent　layers　differentiate　significantly.　Therefore,　in　this　paper,　the　conventional　Laguerre　orthogonal　polynomial　method　is　improved　to　overcome　the　drawbacks.　The　Rayleigh-like　dispersion　curves　of　the　semi-infinite　structure　are　calculated　by　the　improved　method　and　verified　by　the　partial　wave　method.　The　difference　of　the　dispersion　curves　calculated　by　the　conventional　and　the　improved　method　can　be　observed　significantly　for　the　different　adjacent　materials.　As　a　result　of　the　expansion　coefficients　of　the　orthogonal　polynomial,　stress　distribution　is　reconstructed,　and　the　superiority　of　the　improved　method　in　dealing　with　the　continuity　problem　of　boundary　stress　is　verified.　©　2018　Acoustical　Society　of　America.