Mass data traffics, low-latency wireless services and advanced artificial intelligence (AI) technologies have driven the emergence of a new paradigm for wireless networks, namely edge-intelligent networks, which are more efficient and flexible than traditional cloud-intelligent networks. Considering users' privacy, model sharing-based federated learning (FL) that migrates model parameters but not private data from edge devices to a central cloud is particularly attractive for edge-intelligent networks. Due to multiple rounds of iterative updating of high-dimensional model parameters between base station (BS) and edge devices, the communication reliability is a critical issue of FL for edge-intelligent networks. We reveal the impacts of the errors generated during model broadcast and model aggregation via wireless channels caused by channel fading, interference and noise on the accuracy of FL, especially when there exists channel uncertainty. To alleviate the impacts, we propose a robust FL algorithm for edge-intelligent networks with channel uncertainty, which is formulated as a worst-case optimization problem with joint device selection and transceiver design. Finally, simulation results validate the robustness and effectiveness of the proposed algorithm.