Transformerless grid-connected inverters, due to their advantages of high efficiency, small volume and light weight, have been the subject of more research and interest in recent years. Due to the asymmetrical driving signal in pulse width modulation (PWM) caused by time-delay, zero-drift of the current sensors and imparities of the power transistors, output of the grid current contains dc component. As a result, power quality of the grid is degraded. In this paper, a dc (direct current) component suppression scheme with adaptive back-propagation (BP) neural network proportional-integral-differential (PID) control is proposed for dc component minimization. Moreover, sliding-window-double-iteration-method (SWDIM) is utilized for fast dc component extraction. Compared with the conventional method, the proposed scheme shows better performance, and the dc component can be attenuated to be within 0.5% of the rated current.