LCL-filters are widely used in high-power grid-connected inverter system and its inherent resonance should be damped. The change of the equivalent grid impedance under weak grid, the delay of sampling and the lag of the control in the digital control will make regular damping scheme not applicable. This paper presents a method using full-state feedback for LCL-filter grid-connected converters under the weak grid. And the general methodology for poles assignment is addressed with design examples. Three restrictions of poles placement and restrictive inequality are offered. Simulation and experimental results are given for validation.