We improve upon the simple method of Singh et al. [Phys. Rev. B 53, 15 909 (1996)] to calculate the biexciton binding energy in quasi-two-dimensional (2D) quantum wells. Optimizing the geometric configuration, a simple and analytical expression for the ratio of the binding energy of a 2D biexciton to that of an exciton, Ebxx/Ebx, is derived. It is found that the geometric configuration of a positronium-molecule-like biexciton is a square and that of a hydrogen-molecule-like biexciton is a tetragon. The average interparticle distances as functions of σ are also determined. The theory is applied to GaAs, ZnSe, and CdxZn1-xSe quantum wells and the result of Ebxx/Ebx thus obtained agrees with the experimental results.