<p>Multivariate multi-step time series prediction (MTSP) aims to predict the future time steps based on the historical data from multiple variables, but faces challenges such as complex dependencies between variables and error accumulation, leading to poor prediction accuracy. In this study, an attention-based multi-column neural network (AMCNN) for multivariate MTSP is proposed to improve the prediction accuracy. First, an attention mechanism is developed to reconstruct the inputs, highlighting the contribution of important variables to the prediction. Second, to obtain the optimal task allocation for MTSP, an improved binary particle swarm optimization (BPSO) algorithm is designed with the fitness function comprehensively evaluating the MTSP results in terms of both prediction error and shape difference. Finally, a direct-connected adaptive radial basis function neural network (DCA-RBFNN) is constructed as the subnetwork of AMCNN to improve the accuracy with fewer training iterations. Several experiments are performed on two benchmark datasets and two real-world datasets to verify the effectiveness of AMCNN in MTSP. The results demonstrate that AMCNN achieves the best modeling accuracy compared to other models, especially when the prediction horizon is larger, highlighting its superiority for long-term prediction. Positive effects on prediction accuracy have been further demonstrated from the perspectives of the attention-based reconstruction of inputs, the improved BPSO algorithm, and the design of the subnetwork, respectively. Besides, the subnetwork in ACMNN, that is, DCA-RBFNN, contributes to the accurate prediction with fewer training iterations.</p>