The best thing you can do is stay calm. Unlike that kicking, screaming child in your shopping cart, you have the ability to control your emotions and restore the peace.

You can’t bring your toddler to his senses by raising your voice or making threats. Getting mad will only escalate his emotions. You don’t want to cave in, either. If your child is screaming because you passed up the candy aisle, don’t make a U-turn just to calm him down.

Instead, tell him firmly that he has to stop throwing a fit. If he keeps it up, it’s time to use your most potent weapon: the exit door. Even if you’re in the middle of a big shopping trip, you can always whisk your child out of the store. Children like to shop, and there’s a good chance he’ll calm down once he understands the consequences. If he continues throwing a fit, take him home, if possible. The shopping can probably wait.

Keep in mind that children are more likely to lose their tempers when they’re hungry or tired. If you’re about to embark on a marathon shopping trip, try to make sure your child is tanked up and well-rested. It’s also a good idea to establish the ground rules before you reach the store. If he’s likely to lobby for a new toy, you can explain ahead of time that you’re only there to buy groceries.

Frustration is also a big tantrum-producer. If you know your child is going to insist on visiting the pet store when you go to the mall, make sure you have time to do it or think twice about the trip. Thinking through his probable reactions, the consequences, and the alternatives isn’t really “giving in” to him, it’s being a wise parent.

Because he’s out of control, a tantrum can be scary for a child. Once it subsides, give your toddler hugs and reassurance. It’s fine to acknowledge his feelings. You might try to make leaving less painful by offering to read a favorite story when you get home.

Keep in mind that your child’s tantrum is nobody’s business but yours. Your toddler will have tantrums, and some of them are bound to happen in public. It doesn’t mean you’re a bad parent, only that you’re the parent of a toddler.

If you handle the situation with calm and grace, expect to see a lot of knowing glances and sympathetic smiles. Regardless of any looks you get, remember that your child doesn’t understand your embarrassment. Public tantrums aren’t meant to humiliate parents, so you should treat your child the same way as if the tantrum happened at home.        

To tackle Tantrums see the article – Tantrums: Why they happen and what to do about them

Source: http://www.babycenter.com/404_im-embarrassed-by-my-childs-public-tantrums-what-can-i-do_6894.bc?scid=preschooler_20100525:2&pe=2UdYc1a