The series ac capacitor has recently been used with the transformerless grid-connected converters in the distribution power grids. The capacitive characteristic of the resulting series LC filter restricts the use of conventional synchronous integral or stationary resonant current controllers. Thus this paper proposes a fourth-order resonant controller in the stationary frame, which guarantees a zero steady-state current tracking error for the grid converters with series LC filter. This method is then implemented in a three-phase experimental system for verification, where the current harmonics below the LC filter resonance frequency are effectively eliminated. Experimental results confirm the validity of the proposed current control scheme.