Effects of strain on the electronic and optical properties of graphene on monolayer boron nitride (BN) substrate are investigated using first-principle calculations based on density functional theory. Strain-free graphene/BN has a small band gap of 97 meV at the K point. The magnitude of band gap increases with in-plane biaxial strain while it decreases with the perpendicular uniaxial strain. The ε2(ω) spectrum of graphene/BN bilayer for parallel polarization shows red and blue shifts by applying the in-plane tensile and compressive strains, respectively. Also the positions of peaks in the ε2(ω) spectrum are not significantly changed under perpendicular strain. The calculated results indicate that graphene on the BN substrate has great potential in microelectronic and optoelectronic applications.