The electrical characteristics of band-gap engineered tunneling barriers consisting of thin $SiO_2$ and $Si_3N_4$ dielectric layers were investigated for nonvolatile memory device applications. The band structure of band-gap engineered tunneling barriers was studied and the effectiveness of these tunneling barriers was compared with the conventional tunneling $SiO_2$ barrier. The band-gap engineered tunneling barriers composed of thin $SiO_2$ and $Si_3N_4$ layers showed a lower operation voltage, faster speed and longer retention time than the conventional $SiO_2$ tunnel barrier. The thickness of each $SiO_2$ and $Si_3N_4$ layer was optimized to improve the performance of non-volatile memory.