In this article, a fuzzy floating centroids method (FFCM) is proposed, which uses a fuzzy strategy and the concept of floating centroids to enhance the performance of the neural-network classifier. The decision boundaries in the traditional floating centroids neural-network (FCM) classifier are "hard." These hard boundaries force a point, such as noisy or boundary point, to be assigned to a class exclusively, thereby frequently resulting in misclassification and influencing the performance of optimization methods to train the neural network. A fuzzy strategy combined with floating centroids is introduced to produce "soft" boundaries to handle noisy and boundary points, which increases the chance of discovering the optimal neural network during optimization. In addition, the FFCM adopts a weighted target function to correct the preference to majority classes for imbalanced data. The performance of FFCM is compared with ten classification methods on 32 benchmark datasets by using indicators: average F -measure (Avg.FM) and generalization accuracy. Also, the proposed FFCM is applied to nondestructively estimate the strength grade of cement specimens based on microstructural images. In the experimental results, FFCM achieves the optimal generalization accuracy and Avg.FM on 17 datasets and 21 datasets, respectively; FFCM balances precision and recall better than its competitors for the estimation of cement strength grade.