There are many factors that affect the compressive strength of concrete. The relationship between compressive strength and these factors is a complex nonlinear problem. Empirical formulas commonly used to predict the compressive strength of concrete are based on summarizing experimental data of several different mix proportions and curing periods, and their generality is poor. This article proposes an improved artificial bee colony algorithm (IABC) and a multilayer perceptron (MLP) coupled model for predicting the compressive strength of concrete. To address the shortcomings of the basic artificial bee colony algorithm, such as easily falling into local optima and slow convergence speed, this article introduces a Gaussian mutation operator into the basic artificial bee colony algorithm to optimize the initial honey source position and designs an MLP neural network model based on the improved artificial bee colony algorithm (IABC-MLP). Compared with traditional strength prediction models, the ABC-MLP model can better capture the nonlinear relationship of the compressive strength of concrete and achieve higher prediction accuracy when considering the compound effect of multiple factors. The IABC-MLP model built in this study is compared with the ABC-MLP and particle swarm optimization (PSO) coupling algorithms. The research shows that IABC can significantly improve the training and prediction accuracy of MLP. Compared with the ABC-MLP and PSO-MLP coupling models, the training accuracy of the IABC-MLP model is increased by 1.6% and 4.5%, respectively. This model is also compared with common individual learning algorithms such as MLP, decision tree (DT), support vector machine regression (SVR), and random forest algorithms (RF). Based on the comparison of prediction results, the proposed method shows excellent performance in all indicators and demonstrates the superiority of heuristic algorithms in predicting the compressive strength of concrete.