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).
