China Railway Construction, which built the rail link to Tibet, plans to list shares on the Hong Kong and Shanghai stock markets, state media have said.
The firm will issue 2.8 billion shares in Shanghai and at least 1.8 billion in Hong Kong, according to China's official Xinhua news agency.
It plans to use the cash raised to expand construction capability.
Another major railway firm, China Railway Group, performed strongly when it floated last month.
It attracted strong interest as investors tap the country's railway investment boom.
The report said China Railway Construction also helped build the high-speed Shanghai Maglev train, which whisks people between the city's airport and financial centre.
The high-altitude rail link between China's western Qinghai province and Lhasa opened in July 2006.
In the past, Lhasa could be reached only by plane or after a long, arduous road journey.
Hailed as an engineering feat by Beijing, critics fear it will undermine traditional Tibetan culture.