This paper presents the control method of an LCL filter implemented for a three-phase, voltage-source, grid-connected inverter for not only offering better attenuation of switching harmonics but also for highly damping the resonance. A discrete-time deadbeat current controller with tuned state-feedback gains is proposed to realize the time optimum responses with high control accuracy. In addition, the influences of different grid inductances and switching frequencies of the three-level T-type inverter on the controller gains are discussed. The analytical design of the three dimensional deadbeat controller dealing with the instantaneous space vectors is examined under varying grid inductance. The effectiveness of the optimum feedback gains on the control performance is validated experimentally. The deadbeat controller can provide the fastest response and damp the resonance of the LCL filter at relatively low switching frequency in comparison with the filter size.