For grid-connected LCL-filtered inverters, resonance yields instability and low bandwidth. As a result, careful designs are required. This paper presents a systematic current control structure, where pole assignment consisting of one or more feedbacks is the inner loop, and the outer loop is the direct grid current control. Several other issues are discussed, such as the inner-loop feedback choices, pole-assignment algorithms, robustness and harmonic rejection. Generally, this kind of strategy has three different types according to the inner-loop feedback choices. Among them, a novel pole-assignment algorithm has been proposed, where the inner control maintains four freely-assigned poles which are just two pairs of conjugated poles located at the fundamental and resonance frequencies separately. It has been found that with the different types, the steady-state and dynamic performances are quite different. Finally, simulations and experiments have been provided to verify the control and design of the proposed methods.