Due to the existence of grid impedance, the grid voltage often contains low order background harmonics, which will deteriorate the current quality of grid connected converters. In view of this situation, considering the delay effect and weak grid, the robustness of two single loop control modes of LCL-type grid connected converter, namely grid-side current feedback (GCF) and converter-side current feedback(CCF), is evaluated to improve the current quality of the grid current under distorted grid. Through the analysis and demonstration of above impedance models, CCF has the advantages of excellent stability and excellent power quality. Then, a direct harmonic suppression strategy based on CCF is proposed. The strategy takes the converter side current which contains richer low harmonic content as harmonic information source, and the control effect is more effective than the traditional strategy which uses capacitor current as harmonic information source. Without additional control strategy and controller, the hardware cost is reduced and algorithm complexity is simplified. The simulation and experimental results verify the correctness and feasibility of the theoretical analysis.