Sleep is an essential behavior to prevent the decrement of cognitive, motor, and emotional performance and various diseases. However, it is not easy to fall asleep when people want to sleep. There are various sleep-disturbing factors such as the COVID-19 situation, noise from outside, and light during the night. We aim to develop a personalized sleep induction system based on mental states using electroencephalogram and auditory stimulation. Our system analyzes users' mental states using an electroencephalogram and results of the Pittsburgh sleep quality index and Brunel mood scale. According to mental states, the system plays sleep induction sound among five auditory stimulation: white noise, repetitive beep sounds, rainy sound, binaural beat, and sham sound. Finally, the sleep-inducing system classified the sleep stage of participants with 94.7 percent and stopped auditory stimulation if participants showed non-rapid eye movement sleep. Our system makes 18 participants fall asleep among 20 participants.