Active in airports, roads, and power, India’s GMR, led by founder and chairman G. M. Rao, is right in the middle of the country’s efforts to build up a weak infrastructure. While Rao expects the economy to remain vibrant, he worries that it can’t be developed fast enough to support current economic-growth rates. The chairman, whose roots are in the countryside, is also concerned that not enough has been done to strengthen the rural economy, which above all needs education, roads, and jobs to give villagers a chance to participate in the newfound prosperity.

GMR began almost 30 years ago as a single jute mill in the village of Rajam, in the eastern state of Andhra Pradesh. “Our journey to today’s GMR happened just accidentally,” Rao says. “Whatever opportunity came up, we have taken that opportunity.” Along the way, GMR has been active in banking, insurance, and breweries but left these industries to consolidate around infrastructure.

Along with minority partner Fraport, which manages the Frankfurt airport, in Germany, GMR is leading the effort to modernize Delhi’s international airport. It is also building a new international airport in Hyderabad and expanding the Sabiha Gökçen International Airport, in Istanbul. In addition, it...