Taking advantages of the BP neural network in nonlinear mapping and generalization capabilities for multi-parameter problems, the BP neural networks with three hidden layers were constructed to predict the compressive strength of laminates containing embedded fiber wrinkles. The compressive failure was numerically simulated based on a three-dimensional damage model with the LaRC criterion. The numerical results were used as data samples for the networks training. An algorithm based on the golden section method was proposed to quickly determine the range of the neurons number in the hidden layer of the BP neural networks. Then the best number of the neurons was finally determined by comparing the prediction results and the assessment indicators of different cases. The results show that, the error of the strengths of the laminates with the maximum wrinkle angles of 5.6°,9.9° and 11.4° predicted by the developed BP neural networks are 3.4%, 4.6%, and -0.01%, respectively. The approach developed in the present work to predict the strength of composite materials based on the BP neural networks provides an effective way for the strength evaluation of composite materials in application.