Training algorithms play a crucial role in the training process of feedforward neural networks. This paper proposes an improved honey badger algorithm called QEHBA for training multi-layer perceptron (MLP) neural networks. Firstly, quantum encoding and quantum rotation gates are introduced at the initial stage of the algorithm to enrich diversity of the population. Next, the exploration capability of the algorithm is improved by equilibrium pool strategy. To validate the effectiveness of QEHBA for training MLP, we apply it to eight classification datasets, comparing it with four well-known metaheuristic algorithms. The experimental results demonstrate that proposed QEHBA for training MLP achieves the best comprehensive performance.