The structural and electronic properties of new structural cubic (GaN)$_1$/(ZnO)$_1$ superlattice have been investigated using two different theoretical techniques: the full potential-linearized augmented plane wave (FP-LAPW) method and the linear combination of localized pseudo atomic orbital (LCPAO). The new modified Becke-Johnson (mBJ) exchange potential is chosen to improve the bandgap of the superlattice and effective masses. The bandgap is found to be slightly indirect and reduced from those of pure GaN and ZnO. The origin of this reduction is attributed to the $p-d$ repulsion of the Zn-N interface and the presence of the O $p$ electron. The electron effective mass is found to be isotropic. Good agreement is obtained between two used methods and with available theoretical and experimental data.
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