The binding energy of a biexciton in GaAs quantum-well wires is calculated variationally by use ofa two-parameter trial wavefunction and a one-dimensional equivalent potential model. There is no artificial parameter added in our calculation. Our results agree fairly well with the previous results. It is found that the binding energies are closely correlative to the size of wire. The binding energy of biexcitons is smaller than that of neutral bound excitons in GaAs quantum-well wires when the dopant is located at the centre of the wires.