In the present work, we provide the calculation of the 1s-like binding energy of shallow-donor impurity in symmetric double coupled quantum wells based on non-polar wurtzite (In,Ga)N/GaN. Considering the effective-mass and dielectric mismatches, numerical calculations are performed within the framework of parabolic band and single band effective-mass approximations under the finite potential barrier using finite difference method. The pressure- and Indium-dependent binding energy are principally associated with the effective-mass, dielectric constant, quantum size and potential barrier changes. Our main findings show that the predicted binding energy: (i) is enhanced (dropped) with hydrostatic pressure for large (thin) well, (ii) is declined with wells coupling, (iii) is improved (insensitive) with In-composition for thin (large) well and (iiii) is strongly-modulated by the impurity position.