According to the effect of the interlayer interaction of the boron nitride sheet on electronic properties, especially the energy band gap of the graphene sheet in the boron nitride-graphene (BN-G) bilayer, we propose a gapless graphene-based field effect transistor (FET). It is comprised of a boron nitride layer on top of graphene in the channel region. In this study, we investigate the transfer characteristic and output characteristic of the proposed device for different values of the interlayer distance of (BN-G) bilayer. Also, we compare the output results with simulated bilayer graphene channel FET. We find that the I-on/I-off ratio in the proposed device shows a significant promotion compared to graphene bilayer channel FET. Our first-principles calculations show that by decreasing the inter-layer distance of (BN-G) bilayer, the energy gap increase which leads to a dipper I-off current and an increase of I-on/I-off ratio up to 104 for an inter-layer distance of 2.7 angstroms. Moreover, it is found that the proposed device output characteristic displays a very good saturation due to improved pinch-off of the channel.