A multi-layered composite with exceptionally high electromagnetic wave-absorbing capacity and performance stability was fabricated via the facile electrophoresis of a reduced graphene oxide network on carbon nanotube (CNT)-Fe3O4-polyaniline (PANI) film. Minimum reflection loss (RL) of -53.2 dB and absorbing bandwidth of 5.87 GHz (< -10 dB) are achieved, surpassing most recently reported CNT- and graphene-based absorbers. In particular, comparing to the original composites, the minimum RL and bandwidth (< -10 dB) maintains 82.5% and 99.7%, respectively, after 20 h charge/discharge cycling, demonstrating high environmental suitability.