A novel type of vertical graphene micro-ribbons-based three-dimensional frequency selective surface (FSS) is demonstrated to realize dynamic tunability of the frequency selectivity in both center frequency and bandwidth. Different from most available graphene-based FSSs, whose substrates are vertical to the incident direction, in the proposed FSS the substrate is parallel to the incident direction, which results in a small insertion loss for the passband. A stopband is obtained at the plasmon resonant frequency of the graphene micro-ribbons. An equivalent circuit model of the proposed FSS is derived. Additionally, according to the scaling law, the transmission zero frequency can be predicted rapidly and accurately. Based on the combination of the equivalent circuit model and scaling law, the transmission property of the FSS structure is analyzed. Finally, it is shown that the bandwidth of the proposed FSS can be easily extended by a hybrid electrostatic bias.