By fabricating a split gate on the surface of AlxGa1-xAs/GaAs heterostructure，we experimentally obtain a quasi-one-dimensional quantum wire. This structure could be used to implement single-electron transport driven by surface acoustic waves. Based on structures of conduction band and distribution of electrons in the fabricated quantum wires，the influence of quantum-wire widths on the confining potential of the electrons is also discussed. Especially，we numerically study how the linear electron concentration depends on the applied split-gate voltage. For the quantum wires fabricated，we find that the calculated pinch-off voltages agree well with the relevant experimental values measured at 0.3K.