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As the grid impedance increases, the grid strength gradually becomes weak. In order to have good output characteristics in weak grid, grid-forming (GFM) inverters with LCL filter have gradually become popular. This paper studies grid-current-sensorless control which does not require grid current sensors. Firstly, the grid-current-sensorless control loops are given. Then, in order to make up for the inability to sample the actual grid current, a grid current estimator, which is derivative operator free and low-complexity, is proposed. And the robustness and accuracy of the estimator is verified by simulation. Afterwards, to demonstrate that this control operates stably when the grid strength changes, a joint small-signal stability analysis combining the control strategy and circuit topology is presented. The theoretical feasibility of the control is proved. Finally, to verify the robustness of the control under different grid strengths, the experiments are carried out on a 20kW GFM inverter. The results show that the proposed control has satisfactory steady-state and dynamic performance whether under strong grid or weak grid. • The proposed method is suitable for both strong and weak grids. • The proposed current estimator has low complexity. • The proposed method reduces the use of sensors and reduces the hardware cost. [ABSTRACT FROM AUTHOR]