Lattice mismatch and atomic structure studies of InxGa1-xAs/InyAl1-yAs coupled double-step quantum wells have been performed by transmission electron microscopy (TEM) and electron-diffraction pattern measurements. The high-resolution TEM image of the InxGa1-xAs/InyAl1-yAs coupled double-step quantum well showed that two sets of a 60-Angstrom In0.65Ga0.35As deep quantum well and a 60-Angstrom In0.35Ga0.47As shallow step quantum wells bounded by two thick In0.52Al0.48As barriers are separated by a 38-Angstrom In0.52Al0.48As embedded potential barrier, The selective-area electron-diffraction pattern obtained from TEM measurements on the InxGa1-xAs/InyAl1-yAs double-step quantum well showed that InxGa1-xAs active layers were grown pseudomorphologically on the InP buffer layer. The value of the lattice mismatch between the In0.53Ga0.47As and the In0.65Ga0.35As layers obtained from the high-resolution TEM measurements is 1.6%. A possible crystal structure for the InxGa1-xAs/InyAl1-yAs coupled double-step quantum well is presented based on the TEM results. These results can help improve understanding of the structural properties for the applications of strained InxGa1-xAs/InyAl1-y. As coupled double-step quantum wells in new kind of the optoelectronic devices.