I am planning to send money from my US Account to "my" account in a foreign country (I understand that I have to file Form FBAR).
Then, I am going to gift money to my mom who is living in a foreign country.

1) Am I subject to any tax in the US?
2) In case I am subject to a gift tax in the US, can I loan (for example) $24000 to my mom this year and forgive the loan by $12000 each year so I am not subject to any gift tax?
3) Is forgiving a loan by $12000 each year and treating it as gift permitted?

You file Form FBAR (form number is TD F 90-22.1) only if you will keep your money in a foreign country. If you are gifting money to a foreign person, you do not file FBAR.

You can gift $12,000 each year to your mom without filing gift tax return. Give $12,000 on or before December 31, 2008 and another $12,000 on or after January 1, 2009.
If you are married, your spouse can also give another $12,000 to the same person.

Again, as noted in earlier postings, the filing of a gift tax return does NOT mean you must pay gift taxes.

Understand that gift taxes and estate taxes are linked, in that both access the Unified Credit available to the estate. The exact amount of the Unifed Credit changes each year, but the net effect is that the first $2 million of the estate is exempt from estate taxes.

This credit can be accessed using the gift tax return to avoid paying gift taxes.

To answer the questions posed:

1) Yes, gift tax, but see answers below.

2) This is a good and perfectly legal method of transfer $24,000 to your mother tax-free.

3) Yes, it is permitted, and it is a strategy I advise high net-worth parents use to transfer money to the children for large purchases like a hew house.

Dear MutKatA,
Thank you for your reply. you mentioned that I don't have to file Form FBAR. The Form says that if I have more than $10000 "any" time during the year, I have to file the form. I will have more than $10000 in a foreign bank account for at least a day before the money is transferred to my mom. Do I still not file the Form?

If you are directly sending money from your U.S. bank account to your mom's account, you do not file FBAR. If it hits your own account in a foreign country, you file FBAR.

If you want to avoid a taxable gift, you need to be careful with loaning money to a family member and then having portions of the loan forgiven annually. The following is an excerpt from Miller v. Commissioner 71 TCM 1674 (1996):
[Taxpayers] bear the burden of proving that [the IRS's] determinations are erroneous. . . . The question whether a taxpayer has entered into a bona fide creditor-debtor relationship pervades the Federal tax law. . . . "Transactions within a family group are subject to special scrutiny, and the presumption is that a transfer between family members is a gift". . . . That presumption may be rebutted by an affirmative showing that at the time of the transfer the transferor had a real expectation of repayment and an intention to enforce the debt. . . . The mere promise to pay a sum of money in the future accompanied by an implied understanding that such promise will not be enforced is not afforded significance for Federal tax purposes . . .