"The plan is to exceed the Dh2 billion mark for the fund which will close in four to six months," Karim el-Solh said at a news conference on Wednesday.
GC Equity Partners II, which launched late in 2008 with Credit Suisse Alternative Investments, raised two thirds of the fund from international investors.
The global financial crisis has slowed economies across across the Gulf Arab region, but countries are still sitting on surplus revenues amassed from an oil-price rally that saw crude prices hit a high near $150 a barrel in July.
"The speed of investment surprised us, because two thirds of the investments came from international investors which is indicative that the region is attracting foreign direct investment," Solh said.
Stock markets in the Middle East and North Africa have been hard hit by global turmoil and valuations have dropped.
Private equity funds in the region have $11 billion to invest after raising a record $6.4 billion in 2008, the Gulf Venture Capital Association said.
The fund will focus on buying stakes in established firms across the Gulf Arab region in sectors including oil, gas, power, water, healthcare and education.
Solh said it was in advanced discussions to complete a private equity deal in the healthcare sector in a month.