We have theoretically studied the Goos-Hänchen (GH) shifts of both the reflected and transmitted probe beams emerging from a cavity consisting of a hybrid system of a coupled quantum dot (QD) nanostructure and a metallic nanoparticle (MNP). It is realized that the GH shifts in the transmitted and reflected light beams can be enhanced due to the surface plasmon effect in the MNP. Also, it is shown that by adjusting the distance between QD and MNP and polarization control between probe field and major axis of the hybrid system, the simultaneous negative and positive GH shifts in reflected and transmitted light beams can occur. Moreover, the effects of the intensity and detuning of the coupling light on the GH shift properties of the reflected and transmitted lights have been discussed. We have found that under different parametric conditions of the hybrid system, the GH shifts of the reflected and transmitted light beams can be adjusted by tuning the intensity and controlling the detuning of the coupling field. The results show that our proposed model may be used for future optical sensor devices based on MNP hybrid systems.