Electrical properties of AlyGa1-yN/AlxGa1-xN/AIN/GaN structure are investigated by solving coupled Schrodinger and Poisson equation self-consistently. Our calculations show that the two-dimensional electron gas (2DEG) den-sity will decrease with the thickness of the second barrier (AlyGa1-yN) once the AIN content of the second barrier is smaller than a critical value yc, and will increase with the thickness of the second barrier (AlyGa1-yN) when the critical AIN content of the second barrier yc is exceeded. Our calculations also show that the critical AlN content of the second barrier yc will increase with the AlN content and the thickness of the first barrier layer (AlxGa1-xN).