We consider a broadband over-the-air computation empowered model aggregation scheme for federated learning (FL) in Industrial Internet of Things systems. Due to fading and communication noise, the received global gradient parameters inevitably become inaccurate, leading to a notable decrease of the learning performance. Instead of discarding any edge nodes to reduce the aggregation error, we propose to assign each of them a proper weight coefficient in the model aggregation procedures, i.e., amplitude alignment of the received local gradient parameters from different edge nodes is not required in this paper. We derive an upper bound on the performance loss of the proposed FL scheme, which is shown to be related to the weight coefficients of edge nodes and the mean-squared error (MSE) between the desired global gradient parameters and the actually received ones. Then, we derive a closed-form expression for MSE and use it as the objective function to formulate an optimization problem with respect to the edge nodes’ transmit equalization coefficients, their weight coefficients, and the receive scalars of the cloud server. We transform the formulated optimization problem into a convex one and solve it optimally using CVX. Last, we leverage the popular MNIST dataset and conduct experiments to evaluate the prediction accuracy of the proposed FL scheme. Simulation results demonstrate its superior performances.