We present a new method to suppress dramatically the group-III inter-diffusion of InGaNAs/GaAs quantum wells (QWs) during thermally annealing. By inserting a thin compressively strained layer (so-called diffusion-suppressing layer (DSL)) of InxdGa1-xdNydAs1-yd on either side of an InxqGa1-xqNyqAs1-yq QW, both the interdiffusion of In/Ga and photoluminescence (PL) blue shift are decreased significantly and the interfaces of the InGaNAs/GaAs(N) QW is much sharper after the same annealing operation. By detail PL and X-ray diffraction investigation of InGaAs/GaAs QWs, InGaNAs/GaAs QWs with and without DSLs, we believe that the strain at interfaces plays an important role on group-III interdiffusion. It was also found that a small amount of N incorporated in InGaAs/GaAs QW increased the In/Ga interdiffusion. The group-V interdiffusion was observed to be much less than that of group-III.