  In this work, we obtain the Schr\"odinger equation solutions for the Kratzer
potential plus screened Coulomb potential model using the series expansion
method. The energy eigenvalues is obtained in non-relativistic regime and the
corresponding unnormalized eigenfunction. Three special cases were obtained. We
applied the present results to calculate heavy-meson masses of charmonium and
bottomonium , and we got the numerical values for 1S, 2S, 1P,2P, 3S, 4S ,1D,2D
and 1F states. The results are in good agreement with experimental data and the
work of other researchers.
