Based on ferromagnetic germanene, we theoretically propose a multichannel depletion-type field-effect transistor (FET) operated by a vertical electric field. The electron transport properties of the topological transistor are investigated through the nonequilibrium Green's function method. The results reveal that new edge channels can be formed by removing some $\mathrm{Ge}$ atoms along the $x$ axis of the device. The proposed multichannel ferromagnetic germanene transistor has a twice on-state current and half subthreshold swing than that of traditional germanene FETs. Under the coaction of electric induced staggered potential and staggered exchange field, both the $100\mathrm{%}$ spin-polarized edge states and valleys can be achieved. The ferromagnetic germanene FET can be turned off just by adjusting the electric field. In the low electric field conditions, the switching-off mechanism is due to spin blocking caused by the edge-state mismatch, while for relatively high electric field cases, both the edge-state mismatch and energy-valley mismatch are utilized. With the moderate increase in the exchange field, the switching mechanism is not changed, but the threshold electric field and breakdown voltage of the FET can be, respectively, reduced and enhanced significantly. All the results indicate that the proposed ferromagnetic germanene FET is a promising candidate for ultra-low-power dissipation topological devices.