High level penetration of renewable energy sources has reshaped modern electrical grids. For the future grid, distributed renewable power generation plants can be integrated in a larger scale. Control of grid-connected converters is required to achieve fast power reference tracking and further to present grid-supporting and fault ride-through performance. Among all of the aspects for converter control, the inner current loop for grid-connected converters characterizes the system performance considerably. This paper proposes a unified current loop tuning approach for grid-connected converters that is generally applicable in different cases. A direct discrete-time domain tuning procedure is used, and particularly, the selection of the phase margin and crossover frequency is analyzed, which acts as the main difference compared with the existing studies. As a general method, the approximation in the modeling of the controller and grid filter is avoided. The effectiveness of the tuning approach is validated in both simulation and experimental results with respect to power reference tracking, frequency and voltage supporting.