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In this work, we have reported the tunable band gap of single-layer graphene (SLG) on hexagonal boron nitride (h-BN) monolayer arranged in B3 super-lattice form, as a function of an external electric field perpendicular to the super-lattice plane and an applied external bidirectional stress from the first principle Density Functional Theory. To reduce the effect of substrate related performance degradation and open a band gap, graphene placed on h-BN has been reported in literature. To tailor the band gap, perpendicular electric field and biaxial stress were applied in this work. It was observed that band gap increases from compressive to tensile biaxial strain when no electric field was applied. With the application of 5× 10 9 V/m external electric field a band gap of 144.5 meV was found which is promising for logic FET with a trade off in degradation in Fermi velocity and higher electron effective mass.