as a citizen of the united states,can i petition for my grandmother to enter the united stastes ?
As a US Citizen the only family members you can petition for permanent resident status are your parents, your spouse, your children and your siblings. Unfortunately you cannot petition for a grandparent or any other relative. However, you could help your grandmother come in as a visitor for a period of 6 months. Basically you do so by showing that you will provide her with room and board and that you have the income and means to support her while she is here. It doesn't of course guarantee that she will be granted a visit visa but it will help.
If your grandmother's child is a U.S. citizen, then he or she can petition for her.