Analytical expressions for the rotational-vibrational energy levels of diatomic molecules represented by the Tietz-Hua rotating oscillator are derived using the Hamilton-Jacoby theory and the Bohr-Sommerfeld quantization rule. In molecules with moderate and large values of rotational and vibrational quantum numbers, the levels are in much better agreement with the results of numerical calculations than the energies obtained from the common model of the rotating Morse oscillator.