A variational method combined with a numerical computation is adopted to investigate binding energies of excitons in wurtzite AlGaN/GaN double quantum wells. The strain modification on material parameters and the built-in electric fields (BEFs) produced by spontaneous and strain-induced piezoelectric polarization are taken into account. The dependences of excitonic binding energies on the structural dimension including the widths of asymmetric wells and central barrier are presented. The results indicate that the BEF, which is very strong and can be exactly modulated by the structural dimension, plays a dominant role in determining the binding energy. The exciton is almost indirect one for an asymmetric well influenced by the BEF. The binding energy is very small and is insensitive to the structural dimension. The variation of binding energy versus the widths of both the wells and central barrier in an asymmetric structure is rather different from that in a symmetric one.