The Hanoi-based firm, fully known as the Vietnam National Petroleum Group, has sought to list all the 1.29 billion shares, representing its registered capital of VND12.94 trillion (US$568 million), the Industry and Trade Ministry said in a statement.
Petrolimex submitted its listing application on March 10, the exchange said but gave no dates for the debut.
Earlier this month Petrolimex Chairman Bui Ngoc Bao told Reuters the firm expected to debut around April 10-12, while it has yet to set the starting price for the stock.
At its IPO in late July 2011, Petrolimex raised US$20 million via selling nearly 27.43 million shares, or 2.56% of the company, valuing itself at around US$780 million.
Last year, Japan's JX Nippon Oil & Energy bought 8% of stake in Petrolimex for $178 million, making it the strategic investor in the Vietnamese firm and raising the firm's value to US$2.23 billion.
The government still owns a majority of shares in Petrolimex.
Vietnam separates IPOs and stock debuts as two processes. Investors' interest has waned in many major firms because they have largely avoided a government requirement to list within one year of their partial-privatization, which Hanoi describes as "equitization".
Last October the government urged privatized state-owned enterprises to speed up share listing, signalling effort to address investors' complaints over the slow process and to increase corporate transparency.
With a nationwide sale network, Petrolimex owns half of Vietnam's market for distributing oil products. It also deals with insurance and invests in producing equipment for the energy sector.
Last year Petrolimex bagged VND5.17 trillion in its net profit, a jump of 49% from 2015, based on the firm's financial report.
Petrolimex has projected a gross profit growth of 10% this year, the industry ministry's statement said.