One-class classification has been found attractive in many applications for its effectiveness in anomaly or outlier detection. Representative one-class classification algorithms include the one-class support vector machine (SVM), Naive Parzen density estimation, autoencoder (AE), etc. Recently, the one-class extreme learning machine (OC-ELM) has been developed for learning acceleration and performance enhancement. But existing one-class algorithms are generally less effective in complex and multi-class classifications. To alleviate the deficiency, a multilayer neural network based one-class classification with ELM (in short, as ML-OCELM) is developed in this paper. The stacked AEs are employed in ML-OCELM to exploit an effective feature representation for complex data. The effective kernel based learning framework is also investigated in the stacked AEs of ML-OCELM, leading to a multilayer kernel based OC-ELM (in short, as MK-OCELM). The MK-OCELM has advantages of less human-intervention parameters and good generalization performance. Experiments on 13 benchmark UCI classification datasets and a real application on urban acoustic classification (UAC) are carried out to show the superiority of the proposed ML-OCELM/MK-OCELM over the OC-ELM and several state-of-the-art algorithms.