The stability of passive damping of grid-side current feedback control and inverter-side current feedback control of LCL grid-connected inverter is analyzed. From the perspective of domain poles, the position of two conjugate complex roots determain the direction of root locus. Then affect the stability of systems. Digital time-delay is essentially a series correction, revealing that the delay changes control system phase characteristics. The phase lag of the digital delay is beneficial to system stability in some cases, but it depends on resonance frequency, switching frequency and the position of current sensor which is utilized for feedback variable. The paper designs the current controller parameters in the discrete domain. Given that engineering practicality, a method to determine controller parameters quickly is obtained. The theoretical analysis is validated by simulation and experimental results.