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Virtual reality (VR) is a computer technique that creates an artificial environment composed of realistic images, sounds, and other sensations. Many researchers have used VR devices to generate various stimuli, and have utilized them to perform experiments or to provide treatment. In this study, the participants performed mental tasks using a VR device while physiological signals were measured: a photoplethysmogram (PPG), electrodermal activity (EDA), and skin temperature (SKT). In general, stress is an important factor that can influence the autonomic nervous system (ANS). Heart-rate variability (HRV) is known to be related to ANS activity, so we used an HRV derived from the PPG peak interval. In addition, the peak characteristics of the skin conductance (SC) from EDA and SKT variation can also reflect ANS activity; we utilized them as well. Then, we applied a kernel-based extreme-learning machine (K-ELM) to correctly classify the stress levels induced by the VR task to reflect five different levels of stress situations: baseline, mild stress, moderate stress, severe stress, and recovery. Twelve healthy subjects voluntarily participated in the study. Three physiological signals were measured in stress environment generated by VR device. As a result, the average classification accuracy was over 95% using K-ELM and the integrated feature (IT = HRV + SC + SKT). In addition, the proposed algorithm can embed a microcontroller chip since K-ELM algorithm have very short computation time. Therefore, a compact wearable device classifying stress levels using physiological signals can be developed.