Our study proposes a novel hybrid active noise control (ANC) system, called HAD-ANC, that combines an adaptive filter with deep neural networks. HAD-ANC employs a cascade design comprising the frequency-domain block least mean square algorithm and two gated convolutional recurrent networks (GCRNs). The first GCRN follows the adaptive filter to handle nonlinear distortion by reducing the residual error of linear filtering and models the reverse of both loudspeaker and secondary path. The second GCRN models the loudspeaker and secondary path to force the adaptive filter to estimate the primary path. Additionally, we utilize a delay-compensated reference signal to consider the causal constraints of frequency-domain ANC system. Experimental results based on NOISEX-92 dataset show that the proposed system outperforms recent ANC methods, enables wideband noise reduction, and indicates robustness to path changes.