When the parameters of a grid-connected system change, whether the active disturbance rejection control (ADRC) strategy can maintain the stability of the connection between the inverter and the weak grid is an issue. First, the equivalent single input single output sequence impedance model of an ADRC grid-connected inverter considering frequency coupling is established, and the Nyquist stability criterion is used to quantitatively analyze the influence of inverter output power, grid short circuit ratio, phase-locked loop and ADRC parameter changes on grid-connected system stability. Second, given the problems of the stability degradation and broadband oscillation of the ADRC inverter under the weak grid caused by the above parameter changes, an ADRC broadband oscillation suppression method with enhanced linear expansion state observer (e-LESO) is proposed. By adding proportional branches and filtering links inside the LESO in the traditional first-order ADRC, the output impedance of the ADRC inverter is reshaped, and the frequency range with positive damping characteristic in the middle frequency band (100 Hz~1 kHz) is widened, so as to enhance the robustness of the ADRC grid-connected inverter and achieve broadband oscillation suppression. Finally, the effectiveness of the proposed method is verified by simulation.