Nucleosomes are the basic units of eukaryotes. The accurate positioning of nucleosomes plays a significant role in understanding many biological processes such as transcriptional regulation mechanisms and DNA replication and repair. Here, we describe the development of a novel method, termed ZCMM, based on Z-curve theory and position weight matrix (PWM). The ZCMM was trained and tested using the nucleosomal and linker sequences determined by support vector machine (SVM) in Saccharomyces cerevisiae (S. cerevisiae), and experimental results showed that the sensitivity (Sn), specificity (Sp), accuracy (Acc), and Matthews correlation coefficient (MCC) values for ZCMM were 91.40%, 96.56%, 96.75%, and 0.88, respectively, and the average area under the receiver operating characteristic curve (AUC) value was 0.972. A ZCMM predictor was developed to predict nucleosome positioning in Homo sapiens (H. sapiens), Caenorhabditis elegans (C. elegans), and Drosophila melanogaster (D. melanogaster) genomes, and the accuracy (Acc) values were 77.72%, 85.34%, and 93.62%, respectively. The maximum AUC values of the four species were 0.982, 0.861, 0.912 and 0.911, respectively. Another independent dataset for S. cerevisiae was used to predict nucleosome positioning. Compared with the results of Wu's method, it was found that the Sn, Sp, Acc, and MCC of ZCMM results for S. cerevisiae were all higher, reaching 96.72%, 96.54%, 94.10%, and 0.88. Compared with the Guo's method 'iNuc-PseKNC', the results of ZCMM for D. melanogaster were better. Meanwhile, the ZCMM was compared with some experimental data in vitro and in vivo for S. cerevisiae, and the results showed that the nucleosomes predicted by ZCMM were highly consistent with those confirmed by these experiments. Therefore, it was further confirmed that the ZCMM method has good accuracy and reliability in predicting nucleosome positioning.