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Due to the presence of redundant and irrelevant features in large-dimensional biomedical datasets, the prediction accuracy of disease diagnosis can often be decreased. Therefore, it is important to adopt feature extraction methodologies that can deal with problem structures and identify underlying data patterns. In this paper, we propose a novel approach called the Anti Coronavirus Optimized Kernel-based Softplus Extreme Learning Machine (ACO-KSELM) to accurately predict different types of skin cancer by analyzing high-dimensional datasets. To evaluate the proposed ACO-KSELM method, we used four different skin cancer image datasets: ISIC 2016, ACS, HAM10000, and PAD-UFES-20. These dermoscopic image datasets were preprocessed using Gaussian filters to remove noise and artifacts, and relevant features based on color, texture, and shape were extracted using color histogram, Haralick texture, and Hu moment extraction approaches, respectively. Finally, the proposed ACO-KSELM method accurately predicted and classified the extracted features into Basal Cell Carcinoma (BCC), Squamous Cell Carcinoma (SCC), Actinic Keratosis (ACK), Seborrheic Keratosis (SEK), Bowen's disease (BOD), Melanoma (MEL), and Nevus (NEV) categories. The analytical results showed that the proposed method achieved a higher rate of prediction accuracy of about 98.9%, 98.7%, 98.6%, and 97.9% for the ISIC 2016, ACS, HAM10000, and PAD-UFES-20 datasets, respectively. [ABSTRACT FROM AUTHOR]