In the present study we have investigated the bound energy levels and intersubband optical transitions in the Tietz-Hua quantum well for a spatially varying effective mass distribution. The energy levels and eigenfunctions are obtained by solving the effective mass equation through a variational approach. The obtained numerical calculations show that the spatially varying effective mass has a significant effect on the subband energies and transitions between the sub bands in the Tietz-Hua quantum well. We conclude that, the energy levels and hence energy differences between the subband states decrease with increasing the stability and uniformity of the effective mass and eventually converge to the results of the constant effective mass. Furthermore, it was found that the size of the Tietz-Hua quantum well has an important effect on optical responses based on the intersubband transitions and additionally, the asymmetrical form of the Tietz-Hua quantum well is more predominant in stable and uniform effective mass case.