Definitely. "Older babies and toddlers often get jealous when their mom holds another baby," says a pediatrician. "It usually happens between 9 and 15 months." "Your baby is used to having all the attention. If there's suddenly someone else to share it with, he/she is going to say, 'Hey! That's my mom!'"
In fact, one study found that babies as young as 6 months express an early form of jealousy. The infants reacted negatively as their mothers "cared for" lifelike dolls instead of them.
The positive side to your baby's jealousy is that it means he or she truly knows who you are and wants your attention. You're bonded. If you haven't seen your baby demonstrate separation anxiety when you leave the room or the house, or stranger anxiety when a new person walks into the room, you probably will soon.
If you and your baby are visiting a friend and you pick up a cuddly newborn and begin cooing at her, it's normal for your baby to possessively demand your attention.
At this age, your baby is too young to understand the concept of sharing Mom. Pass the friend's baby back, pick up your child, and look at the baby together. When your child is distracted by some toys across the room, you can try holding your friend's baby again.
When your child is older, it's important to teach him or her to accept your giving attention to other children. One way to do this is to involve your child right off the bat. Ask, "Should we hold the baby together?" Or say, "I'm going to hold the baby – why don't you help me?" Ask your child to hold the baby's feet or blanket.
If you get your child to participate, he/she will feel appreciated and involved. And remember to praise him/her for doing a great job helping."