This work proposes a new evolutionary multilayer perceptron neural networks using the recently proposed Bird Swarm Algorithm. The problem of finding the optimal connection weights and neuron biases is first formulated as a minimization problem with mean square error as the objective function. The BSA is then used to estimate the global optimum for this problem. A comprehensive comparative study is conducted using 13 classification datasets, three function approximation datasets, and one real-world case study (Tennessee Eastman chemical reactor problem) to benchmark the performance of the proposed evolutionary neural network. The results are compared with well-regarded conventional and evolutionary trainers and show that the proposed method provides very competitive results. The paper also considers a deep analysis of the results, revealing the flexibility, robustness, and reliability of the proposed trainer when applied to different datasets.