I've talked to several pediatricians and they say that thumb sucking should be normal for babies, and it usually lasts until they are toddlers (2-4 years old). For older kids who continue to thumbsuck, you may offer small rewards and always give gentle reminders as part of your positive reinforcement.
Thumbsucking is baby's way to relax so don't be too much worried about it. As for my children, their thumbsucking habit ended before they turned 6 mos. Kusa silang tumigil...
Always remove your baby's hand from his mouth every time he does it. Don't get tired until he eventually stops doing it.
Take his hands away from his mouth whenever he attempts to thumb suck. Eventually, he'll forget doing it.