This paper proposes an improved three-stages cascading passivity-based control (PBC) for a grid -connected LCL converter in unbalanced weak grid condition. In general, the traditional double-loop control based on positive and negative sequence transformations is used in grid-connected converter control in unbalanced weak grid condition. However, it is time consuming for second harmonic filtering, and positive and negative sequence currents need to be controlled separately. The PBC has strong robustness to interference, and the line voltage based PBC can deal with the voltage unbalance effectively and easily without negative sequence transformation. But the traditional PBC needs six variables and three damping coefficients for the grid-connected LCL converter in unbalanced grid condition, and it has the disadvantage of difficult implementation. The improved PBC can realize the same control effect with three-stages cascading PBCs of two variables and one damping coefficient, and it has the advantages of easy implementation, good performance and high stability. First, the modeling and controller design are detailed described. Then the SIMULINK simulation results demonstrate the benefits of the improved control strategy. Finally, a grid-connected LCL converter prototype of 5kW is built and the experimental results verify the correctness and effectivity of the improved three-stages PBC strategy. An Improved Three-Stages Cascading Passivity-Based Control of Grid-Connected LCL Converter in Unbalanced Weak Grid Condition