This study is aimed to the numerical modeling of the surface plasmon-polariton excitation by a layer of active (electrically pumped) quantum dots embedded in a semiconductor, covered with a metal. It is shown that this excitation becomes much more efficient if the metal has a form of a thin (with thickness of several nanometers) film. The cause of this enhancement in comparison with a thick covering metal film is the partial surface plasmon-polariton localized at the metal-semiconductor interface penetration into air. In result the real part of the metal+air half-space effective dielectric function becomes closer (in absolute value) to the real part of the semiconductor dielectric function than in the case of a thick covering metal film. This leads to approaching the point of the surface plasmon-polariton resonance (where absolute values of these parts coincide) and, therefore, the enhancement of the surface plasmon-polariton excitation. The calculations were made for a particular example of InAs quantum dot layer embedded in GaAs matrix covered with an Au film. Its results indicate that for the 10 nm Au film the rate of this excitation becomes by 2.5 times, and for the 5 nm Au film - by 6-7 times larger than in the case of a thick (40 nm or more) Au film.