If I pay the mortgage at my grandmother's house but my name is not on it can I claim it? She does not claim it.

[DoninGA]

Mortgage interest is an itemized deduction.  Unless the Total of all itemized deductions on Schedule A is greater than the Standard Deduction for your filing status there is no need to report the mortgage interest on a tax return.

Additionally, since your name is not on the mortgage you cannot claim the mortgage interest on your tax return.

[JohnB5677]

No!  You must have an ownership interest in the property to deduct interest on a loan. This means that your name has to be on the deed, or you have a written agreement with the deed holder that establishes you have an ownership interest.  You're not allowed to claim the mortgage interest deduction for someone else's debt. 

[Mike9241]

there might be a way to claim the mortgage interest even if you are not on the deed or even liable for the mortgage.  you must meet the conditions of being an equitable owner.

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You may be an equitable owner entitled to deduct your share of the mortgage interest and real estate taxes. An equitable owner is a person who has the economic benefits and burdens of ownership, based on the facts. Occupying and maintaining the home and paying the mortgage and taxes on it are (strong) factors that probably would indicate equitable ownership.   An equitable owner can deduct interest paid on a mortgage even if they are not directly liable on the debt. IRS REG. 1.163-1. Further, mortgage payments and taxes paid from a joint account with two equal owners are presumed to be paid equally by each account owner (absence evidence to the contrary). However, if payments are made from separate funds, each taxpayer is entitled to deduct all the interest and taxes they pay with their separate funds (CCA 201451027).