The propagation characteristics of surface acoustic waves (SAW) in perovskite-type ferroelectric films/MgO/GaAs structures were investigated theoretically. Phase velocities of the layered structure are larger than those of the and PZT/MgO/GaAs layered structures for the same hK value of the perovskite-type ferroelectric film. Large coupling coefficients can be obtained when the interdigital transducer (IDT) is on top of the perovskite-type ferroelectric film, with and without the floating-plane electrode at the perovskite-type ferroelectric film - MgO buffer layer interface; and peak values of the coupling coefficients of the PZT films (2.8 - 3.8%) are higher than those of the (1.9 - 2.5%) and films (1.5 - 2.3%). There exists a minor peak of the coupling coefficients for the PZT and films when the hK value of the perovskite-type ferroelectric film is about 0.5, but not for the films, if the IDT is on top of the perovskite-type ferroelectric film with the floating-plane electrode at the perovskite-type ferroelectric film - MgO buffer layer interface. The minor peak values of the coupling coefficients for both PZT/MgO/GaAs and layered structures all decrease when we increase the hK value of the MgO buffer layer from 0 to 0.25. The results could be beneficial for combining ferroelectric devices, semiconductor devices and SAW devices on the same GaAs substrate.