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In this work, we study the cavity size effect on the eigen-energies of one-dimensional Schroedinger equation for certain diatomic molecules governed by Morse potential interaction confined in the cavity. To avoid the dissociation of the molecule, we have realised the confinement by introducing two barriers on both sides of the minimum of the potential: the first, at the left, is fixed at $ x_{L}=-ln2/\alpha $ x L = − l n 2 / α and the second at the right i.e. $ x_{R}=\lambda _{i}=-ln2/\alpha +\gamma _{i}r_{e} $ x R = λ i = − l n 2 / α + γ i r e where $ \gamma _{i} $ γ i is a parameter that allows us to vary the size of the cavity. It turns out that the confinement gives rise to additional energy levels and that the number of these levels increases with the size of the cavity (i.e. by increasing $ \gamma _{i} $ γ i or by decreasing the confinement). We used Green's function approach and reported our results on $ {\rm H}_{2},{\rm HCl} $ H 2 , HCl and $ {\rm LiH} $ LiH molecules. [ABSTRACT FROM AUTHOR]