In this paper, we analyze and simulate the plasmonic effect on the quantum-dot photodetector responsivity. For this purpose, a plasmonic-based quantum-dot photodetector is designed in which a few quantum dots are embedded in the hot-spot regions of the plasmonic nanoparticles, wherein a high-intensity localized field is created. Notably, due to the maximum overlapping of the plasmonic field with the quantum dots at the hot spot, some of the optical characteristics of the quantum dot, particularly the spontaneous emission decay rate, are changed. This paper focuses on the engineering of the decay rate, through which we found that the quantum-dot photodetector responsivity is strongly enhanced with the order of 100 times at the visible range. For analyzing the proposed system, we first work on the plasmonic effect of the nanoparticle on the quantum-dot lifetime using the Heisenberg-Langevin equations. It is shown that by embedding the quantum dots at the hot spot of the nanoparticle, the decay rate of the quantum dot is dramatically influenced. In the following, plasmonic-quantum dot system responsivity is theoretically examined using a time-varying perturbation theory. Using this approach is necessary because the spontaneous emission cannot be analyzed with the classical methods. Consequently, it is proved that using plasmonic effect leads to enhanced photodetector responsivity, suggesting that even very small incoming signals are detectable.