Yes, this can be claimed as a tax deductible expense. However, you need to demonstrate that your parents and/or grandparents do not have sufficient income themselves and depend on your support. You will need to complete the attached form and have it certified in the country where your parents/grandparents live.
Download the application here:
Unterhaltserklaerung (Maintenance)
This completed form should carry your parent’s/grandparent’s signature, and should be submitted to the German Finanzamt along with proof/evidence of the money transferred (copy of your German bank statement with debit transactions to prove that the money was transferred to the dependent, and the bank statement of the dependent’s bank account as proof that money was received by the dependent). The amount allowed for support depends on the country in which they live. In India, as an example, it is 2496 Euro/year/person.
You cannot, however, claim all of the amount which is sent, only a portion thereof. The amount that can be claimed also depends on your own income. To simplify: if your income is up to 15,340 Euro per year, you can deduct what you pay to your parents, but only for the amount that EXCEEDS 5% of your income (767 Euro if you earn 15,340 Euro per year). In other words, if you earn 15,340 Euro per year and pay your parents 1,000 Euro, you can deduct 233 Euro from your taxes (the amount that exceeds the 5% limit). The next income range is 15,341-51,130 Euro, where you can deduct what you pay which is over 6% of your income, and then 7% for above 51,130 Euro.