The high-power grid-connected inverters with LCL filters have been widely used. Current control plays a key role in the grid-connected inverter control system. To cope with the inherent resonance of the LCL filter, active damping (AD) methods are usually employed. However, the AD performance is impaired by control delays which are introduced in the digital control implementation process. Besides, the lag phase due to control delays limits the system bandwidth and stability margin. The effects of control delays are more noteworthy in the high-power grid-connected inverter due to its low switching frequency. This paper investigates the current control strategy based on multisampling for the high-power grid-connected inverter with the LCL filter. First, the multisampled AD scheme is studied, which can reduce control delays effectively and improve AD performance. Besides, the multisampled control without additional damping whether passive or active is researched. Through the inverter-side current feedback, the system can realize single-current-loop control based on multisampling. Thus, the control system is simplified and it can be stable, and achieve better dynamic performance. Finally, experimental results show that the proposed control schemes are effective.