Classification of normal and malignant cells observed under a microscope is an essential and challenging step in the development of a cost-effective computer-aided diagnosis tool for acute lymphoblastic leukemia. In this paper, we propose the neighborhood-correction algorithm (NCA) to address this challenge, which consists of three major steps, including (1) fine-tuning a pretrained residual network using training data and producing initial labels and feature maps for test data, (2) constructing a Fisher vector for each cell image based on its feature maps, and (3) correcting the initial label of each test cell image via the weighted majority voting based on its most similar neighbors. We have evaluated this algorithm on the database provided by the grand challenge on the classification of normal and malignant cells (C-NMC) in B-ALL white blood cancer microscopic images. Experimental results demonstrate that our proposed NCA achieves the weighted F1-score of 92.50% and balanced accuracy of 91.73% in the preliminary testing and achieves weighted F1-score of 91.04% in the final testing, which ranks the first in C-NMC. Associated code is available at https://github.com/YongshengPan/ISBI-NMC.