  In this work, we obtain the Schr\"odinger equation solutions for the Varshni
potential using the Nikiforov-Uvarov method. The energy eigenvalues are
obtained in non-relativistic regime. The corresponding eigenfunction is
obtained in terms of Laguerre polynomials. We applied the present results to
calculate heavy-meson masses of charmonium and bottomonium .The mass spectra
for charmonium and bottomonium multiplets have predicted numerically. The
results are in good agreement with experimental data and the work of other
researchers.
