In a package mounting structure for mounting a package on a case, wherein the package internally incorporates at least one of a high-frequency transistor, MIC and MMIC used in the microwave to millimeter-wave band, and a base thereof is formed of metal and serves as ground, an electrically conductive sheet having excellent thermal conductivity and exhibiting restorability and having a size identical with that of the base of the package is laid on the case at a package-bearing location, the package and sheet are fastened together by two or more screws, and the sheet is mounted on the case while it is pressed by a pressing force of 10 N/cm.sup.2 or greater owing to fastening.