Magnon transistors that can effectively regulate magnon transport by an electric field are desired for magnonics, which aims to provide a Joule-heating free alternative to the conventional electronics owing to the electric neutrality of magnons (the key carriers of spin-angular momenta in the magnonics). However, also due to their electric neutrality, magnons have no access to directly interact with an electric field and it is thus difficult to manipulate magnon transport by voltages straightforwardly. Here, we demonstrated a gate voltage (V_{g}) applied on a nonmagnetic metal and magnetic insulator (MI) interface that bent the energy band of the MI and then modulated the probability for conduction electrons in the nonmagnetic metal to tunnel into the MI, which can consequently enhance or weaken the spin-magnon conversion efficiency at the interface. A voltage-controlled magnon transistor based on the magnon-mediated electric current drag (MECD) effect in a Pt-Y_{3}Fe_{5}O_{12}-Pt sandwich was then experimentally realized with V_{g} modulating the magnitude of the MECD signal. The obtained efficiency (the change ratio between the MECD voltage at ±V_{g}) reached 10%/(MV/cm) at 300 K. This prototype of magnon transistor offers an effective scheme to control magnon transport by a gate voltage.