In this paper, we investigate how to deploy computational intelligence and deep learning (DL) in edge-enabled industrial IoT networks. In this system, the IoT devices can collaboratively train a shared model without compromising data privacy. However, due to limited resources in the industrial IoT networks, including computational power, bandwidth, and channel state, it is challenging for many devices to accomplish local training and upload weights to the edge server in time. To address this issue, we propose a novel multi-exit-based federated edge learning (ME-FEEL) framework, where the deep model can be divided into several sub-models with different depths and output prediction from the exit in the corresponding sub-model. In this way, the devices with insufficient computational power can choose the earlier exits and avoid training the complete model, which can help reduce computational latency and enable devices to participate into aggregation as much as possible within a latency threshold. Moreover, we propose a greedy approach-based exit selection and bandwidth allocation algorithm to maximize the total number of exits in each communication round. Simulation experiments are conducted on the classical Fashion-MNIST dataset under a non-independent and identically distributed (non-IID) setting, and it shows that the proposed strategy outperforms the conventional FL. In particular, the proposed ME-FEEL can achieve an accuracy gain up to 32.7% in the industrial IoT networks with the severely limited resources.