Due to the effectiveness of anomaly/outlier detection, one-class algorithms have been extensively studied in the past. The representatives include the shallow-structure methods and deep networks, such as the one-class support vector machine (OC-SVM), one-class extreme learning machine (OC-ELM), deep support vector data description (Deep SVDD), and multilayer OC-ELM (ML-OCELM/MK-OCELM). However, existing algorithms are generally built on the minimum mean-square-error (mse) criterion, which is robust to the Gaussian noises but less effective in dealing with large outliers. To alleviate this deficiency, a robust maximum correntropy criterion (MCC)-based OC-ELM (MC-OCELM) is first proposed and then further extended to a hierarchical network to enhance its capability in characterizing complex and large data (named HC-OCELM). The gradient derivation combining with a fixed-point iterative updation scheme is adopted for the output weight optimization. Experiments on many benchmark data sets are conducted for effectiveness validation. Comparisons to many state-of-the-art approaches are provided for the superiority demonstration.