A novel intercarrier interference (ICI)-aware orthogonal frequency division multiplexing (OFDM) channel estimation network ICINet is presented for rapidly time-varying channels. ICINet consists of two components: a preprocessing deep neural subnetwork (PreDNN) and a cascaded residual learning-based neural subnetwork (CasResNet). By fully taking into account the impact of ICI, the proposed PreDNN first refines the initial channel estimates in a subcarrier-wise fashion. In addition, the CasResNet is designed to further enhance the estimation accuracy. The proposed cascaded network is compatible with any pilot patterns and robust against mismatched system configurations. Simulation results verify the superiority of ICINet over existing networks in terms of better performance and much less complexity.