This paper describes the use of the finite difference method to study the binding energy and the structure of a biexciton in a model parabolic quantum wire (QWR). The biexciton binding energies calculated for different QWR widths are compared with recent experimental data and reasonable agreement is obtained. The conditional wave function of the biexciton has been investigated, and the structure of a biexciton in a QWR has been found to be similar to that of the H2 molecule. The pair correlation functions for particles in bound biexcitons have also been calculated, and a clear picture for the particle configuration in a biexciton is established. Through the study of the average interparticle distance in a biexciton, we find that the individual excitons may retain their identity in bound biexcitons.