According to a tight-binding model and the Green's function formalism, we investigate the electronic transport in hybrid contact of doubly stacked zigzag graphene nanoribbons. Our study shows that the next nearest neighbor interlayer coupling, the hybrid contact length and gate voltage each have a significant modulation effect on the electron transmission spectrum. Due to the next nearest neighbor interlayer coupling, the transmission spectrum of the hybrid contact exhibits an electron-hole asymmetry, which is consistent with the experimental result. There exist some transmission gap (T=0) and quantum step (T=1) within the first subband below the Fermi energy, meaning that electrons can reflect and/or transmit completely. It is also observed that the transmission coefficient oscillates within 1 as the contact length increases, showing a quantum interference effect. Under a gate voltage in the bilayer regime, the transmission coefficient can be changed from 1 to 0, showing that a switching effect exists here. The results is useful for the design and the application of the graphene-based device.