This paper describes a Two-step Band-split Neural Network (TBNN) approach for full-band acoustic echo cancellation. Specifically, after linear filtering, we split the full-band signal into wide-band (16KHz) and high-band (16-48KHz) for residual echo removal with lower modeling difficulty. The wide-band signal is processed by an updated gated convolutional recurrent network (GCRN) with U$^2$ encoder while the high-band signal is processed by a high-band post-filter net with lower complexity. Our approach submitted to ICASSP 2023 AEC Challenge has achieved an overall mean opinion score (MOS) of 4.344 and a word accuracy (WAcc) ratio of 0.795, leading to the 2$^{nd}$ (tied) in the ranking of the non-personalized track.