In this paper we report the effect of shell thickness on transmission probabilities of electrons and holes in the strained configuration of zinc-selenide/zinc-sulphide (ZnSe/ZnS) core-shell quantum dot. The transmission probabilities of electrons/holes were calculated within the frame work of effective mass approximation and quantum mechanical tunneling. In the first attempt, we introduced extra deposit shell thickness of ZnS in the range 0-5nm and calculated its size effects on the transmission of carriers from core to the shell. We observed that quantum dot of small size core show superb characteristics of possible transmissions and the transmission probability of the carriers across the potential barrier can be controlled by varying the shell thickness, which has practical significance for electron transport in quantum dots, electron transfer in bio-sensors and chemo-sensors etc. Moreover, it is also found that for higher values of electron/hole energies (greater than 0.7eV), the transmission probability oscillates, which too has practical significance for quantum oscillators.The study is important from both basic and applied point of view.