  Hulth\'en plus Hellmann potentials are adopted as the quark-antiquark
interaction potential for studying the mass spectra of heavy mesons. We solved
the radial Schr\"odinger equation analytically using the Nikiforov-Uvarov
method. The energy eigenvalues and corresponding wave function in terms of
Laguerre polynomials were obtained. The present results are applied for
calculating the mass of heavy mesons such as charmonium and bottomonium . Four
special cases were considered when some of the potential parameters were set to
zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential,
and Hulth\'en potential, respectively. The present potential provides
satisfying results in comparison with experimental data and the work of other
researchers.
