Recently, I noticed that my 2-months-old baby sleep almost a day include naps (maybe 3-5 hours awake). Should I do anything about this? Such as just wake him up or it is normal.
This awesome chart takes data from books like Healthy Sleep Habits, Happy Child and the experience of the members on the forum who developed it. The totals on that chart are generally much greater than those listed by Dr. Ferber in his Solve Your Child's Sleep Problems, but consistent with other sleep books.
Your child's total wake time sounds normal and, more importantly, healthy. Babies really need sleep to grow and process their experiences. The wake time will dramatically increase over the next few months.