If I have received my green card in August 2014, how long do I have to wait to apply for green card for my father?

Regrettably, there is no visa category by which a Lawful Permanent Resident (a "Green Card" holder) may petition for a parent. A Permanent Resident may, however, apply for a parent in the Immediate Relative visa category once the Permanent Resident becomes a naturalized U.S. citizen. Generally one may apply for naturalization as early as 90 days before the end of five years from the date he/she became a Permanent Resident (90 days before the end of three years for most Permanent Residents married to a U.S. citizen). Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

You need to wait for 3 or 5 years depending on the basis for the green card.