An infant and child sleep survey questionnaire was performed in a well-baby clinic to investigate parent-reported sleep problems in the children. A total of 506 children aged 0–6 years were enrolled and divided into five age groups. The results contain important clinical implications, as follows: (i) frequent night waking is observed in 37.5% of the children; (ii) more than 70% of the children take 30 min or longer to fall asleep; (iii) illness interferes with sleep at night in 35.0% of the children; (iv) caregivers’ perceptions of sleep problems is very common (64.2%); (v) the children sleep for a total of between 11.5 and 15.4 h; (vi) they go to sleep between the hours of 21.00 and 22.00 hours; (vii) they wake between 07.00 and 09.00 hours and (viii) the frequency of sleep problems is related to their age, and problems are more prevalent in the going to bed schedule, night waking, and daytime sleepiness. We conclude that sleep problems of infants and young children are very common in northern Taiwan, and the data analysis of sleep problems may provide valuable information to medical personnel and parents in the clinical evaluation and management of sleep problems.