Not long ago I was asked this very good question. The person asking had been baptized in a ceremony as an infant, but had recently come to faith as an adult. He wanted to know if he needed to be baptized again.
Although not everyone baptized as an infant questions this, it is still often asked. As many come to faith and begin to grow in the Lord by reading the New Testament, they often wonder about their infant baptisms. This could suggest that there is something about the baptisms that they read about in the New Testament that causes them to instinctively wonder about its application to the early, post-natal population. Perhaps they feel that there should be a personal joy in baptism in which they had not experienced? In any event, the question is a valid one.
Those who support infant baptism would argue that it would be improper to be baptized again after coming to faith. This is because they hold that the first baptism accomplished that which was intended. They would point out that it had removed original sin, and had come to fulfillment in the person’s life when they came to faith. Therefore, it would be argued that the original baptism was sufficient and a “re-baptism” is out of step with our Christian faith.
Those who hold that infants are not proper candidates for baptism, would simply counter that the pediatric baptism was not valid and that a proper baptism should be offered upon conversion.
Since I do not believe that a Biblical case can be made to support paedobaptism, it is my opinion that it fails to classify as Christian baptism (see my article, Are Babies to Be Baptized?). Therefore, the convert is not getting re-baptized, but in essence becoming baptized for the first time.
I believe that there is a passage of Scripture that may be helpful to consider. It is found in Acts 19:1-7. In that section we find Paul traveling to Ephesus. There, he encountered about a dozen disciples. It is not clear if they were disciples of Jesus, or of John the Baptist, and I think a good argument could be made for either. In any event, as Paul spoke with them he discovered that they had been baptized into John’s baptism, not Jesus’ baptism. So, although they had already experienced a baptism of sorts, Paul decided that they must experience Christian baptism, and so he baptized them into Jesus’ name.
In the same way, I believe that a person who was baptized as a baby, and later came to faith, should be encouraged to undergo water baptism. However, I understand that not everyone is going to agree. Therefore, I strongly recommend that this question be taken to the Lord, and that His Spirit be permitted to provide the final answer. Whatever answer that the Lord gives should be agreeable to all Christians.