The dispersion and attenuation features of the multi-physical fields coupled waves propagating in an infinite piezoelectric semiconductor and the reflection problem at a boundary which is mechanically free, electrically insulation and the dielectrically open circuit are studied in this paper. Different from the classic dielectric piezoelectric medium, there are four kinds of coupled elastic waves, i.e. the quasi-longitudinal wave (QP), the quasi-traverse wave (QSV), the electric–acoustic wave (EA) and the electron or hole carriers wave (CP), in a piezoelectric semiconductor. The influences of the steady carrier density and biasing electric field upon the dispersion and attenuation features of these coupled elastic waves and the reflection amplitude ratios are studied numerically. The energy flux of each wave and the interaction energy fluxes among all waves are also calculated, and the energy flux balance is checked. It is found that the piezoelectric semiconductor behaves like the viscoelastic solid to carry a decaying wave. The steady carrier density and biasing electric field have significant influences on the dispersion and attenuation features and can be used to regulate the propagation of the coupled elastic waves.