It has been demonstrated that the spontaneous emission rate can be enhanced dramatically by Surface Plasmon Polaritons (SPP) due to large density of states for photon near the SPP resonance frequency and very small mode volume. Some valuable works have been reported to verify such effect with a single metal layer above the semiconductor active layer. However, huge power dissipating to "lossy surface wave (LSW)" mode occurs in such monolayer structure because the enhancement decays with the distance away from the interface exponentially and therefore the active layer should be close enough to the metal film. LSW will convert the energy into heat and make the monolayer structure hardly be applied to obtain large enhancement of spontaneous emission. In this paper, we propose a double-layer structure with two metal films at the top and bottom of semiconductor layer. By assuming the dipole (classical model for the source) at the center of the active layer, which means the distance between the dipole and the interfaces is half of the thickness of active layer, the enhancements of spontaneous emission were calculated and analyzed for both monolayer and double-layer structures with different thickness of the metal film and active layer. The calculation results show that, for the double-layer structure, the critical thickness of the active layer, where the power to SPP exceeds the power to LSW, is much thinner than that in the monolayer structure. This means that the active layer can be set closer to the metal film in the double-layer structure without worrying about the LSW. Therefore, larger enhancement of spontaneous emission rate and higher available energy can be achieved simultaneously.