If There is a case where decision trees are getting overfitted so by using gradient boost method do we solve that problem?
If your trees are overfitting you should probably check the hyperparameters of the tree. You shouldn't let the tree have leaves with too few samples, for example, since that would mean that the tree is memorizing every possible outcome of the training set, in other words, it's overfitting. 

Maybe if you share some more information of your case we could help a little further, but I think you now at least have something to check.

Hope this helps!