In this work, the study of the 1s-like exciton states and binding energy is presented for coupled double zinc blende GaN/InGaN quantum wells. The effective mass approximation and a variational procedure are the key theoretical tools used. The significant role of the position-dependent effective mass is highlighted. It is found that the correct inclusion of position-dependent masses is the cause of a noticeable difference in exciton energies with respect to the use of constant effective mass. In addition, the influence of the interaction of electrons and holes with the central barrier, and the effect of its size are particularly discussed.