A three-phase grid-connected inverter, and a method and a device for controlling the three-phase grid-connected inverter are provided. The method is applied to a three-phase three-leg grid-connected inverter. A structure of the three-phase three-leg grid-connected inverter is improved, so that a filter capacitor (C1, C2, and C3) is connected to a negative electrode of a direct current input bus to form a harmonic bypass circuit. Inverter devices connected in parallel in the system operate stably without increase of inductance of an inductor (L1, L2, L3). In addition, the three-phase three-leg grid-connected inverter according to the present disclosure operates in a discontinuous mode of inductor current (iL1, iL2, and iL3). That is, in the process that a power switch transistor (Q1, Q2, Q3, Q4, Q5 and Q6) on bridge legs is turned on, the inductor current (iL1, iL2, and iL3) drops to zero.