I inherited a house in India in 2006 when I was a Green Card Holder. Later in 2008 I became US citizen and I am holding dual citizenship in US and India. Should I report to IRS about the property that was inherited before becoming US citizen? If 'yes', how should I report it and what forms should be used? Is there any penalty for delayed reporting?

Anything (earned income, passive income, inherited property) that happened in another country PRIOR to you becoming a green card holder does NOT need to be reported to the U.S. government.

Yes, you were required to file Form 3520. Complete part IV that covers bequest:
"in law, generally a gift of property by will or testament. The term is used to denote the disposition of either personal or real property in the event of death."

To avoid penalty, you should attach a statement why you did not file in time. This is from instructions to Form 3520:
"Reasonable cause. No penalties will be imposed if the taxpayer can demonstrate that the failure to comply was due to reasonable cause and not willful neglect."

I have to disagree with MukatA on this one.

Any financial transactions which occurred prior to you geeting the Green Card, i.e. you were a non-resident alien, by treaty and under U.S. tax law, does NOT have to be reported to the IRS. You CAN if you wish to report it, but in no way, shape or form is it REQUIRED.

The property was inherited when a GC holder (hence a US person).

It definitely needs to be reported on form 3520 if its FMV was > $100K when inherited. Given that property prices in India are apparently quite high, this threshold was likely crossed.