A novel metal-dielectric semiconductor microdisk laser structure with the thickness of 2 micrometer and the radius of 6 micormeter is designed by depositing a silica film and a noble metal gold film on the InGaAsP semiconductor microdisk. The angle between side-wall surface and the bottom plate is 45°. The whispering gallery mode of the device is numerically investigated by using a well-known Finite Element Method (FEM). The so-called weak-form of the partial differential equation is employed to effectively reduce the pseudo-solution associated with the local invariant, which exists in the FEM directly applying to Maxwell equations.The distribution of the cross magnetic field (TM) of the whispering gallery mode of the proposed microdisk laser is achieved based on the numerical solution of the weak-type vector Helmholtz equation. After that the quality factor (Q), the mode volume and other related quantities are discussed. Theoretical results show that the quality factor of the proposed microdisk laser with the sandwich-structure is 2~3 times more than the one with the structure directly deposited metal film in InGaAsP semiconductor microdisk. Furthermore, different thicknesses of the metal and the dielectric quality factor of the microdisk laser and the relationship between the disk radius and the quality factor are discussed. A fundamental mode and higher-order surface plasma wave mode, and a maximum quality factor of about 5 400 optical-dielectric of the fundamental mode are achieved.