The forecast, reported by the Xinhua News Agency, is below the 2012 rate of 7.7 percent but above the government's 7.5 percent target.
Communist leaders are trying to steer China to slower, more sustainable growth but an unexpectedly sharp decline in 2012 and this year prompted concern about politically dangerous job losses. Beijing temporarily reversed course and shored up growth in mid-2013 with a mini-stimulus of higher spending on building railways and other public works.
China has the strongest economic growth of any major country but this year's forecast rate is barely half of 2009's 14.2 percent.
In a report to China's ceremonial legislature, the Cabinet warned that growth faces challenges including rising labor costs, environmental problems, weak global demand and excess production capacity in some industries, according to Xinhua.
"We cannot deny a downward pressure on economic growth," the minister in charge of the Cabinet's planning agency, Xu Shaoshi, was quoted as saying.
The report cited potential problems including slow economic restructuring, worsening pollution and "social conflicts among interest groups," Xinhua said.
The government will continue to reduce excess production capacity in industries including steel, cement, aluminum and glass in which supply exceeds demand, Xinhua said. The glut of supply in those fields has led to price-cutting wars that threaten the financial health of companies.
Chinese leaders are under pressure to replace a growth model based on exports and investment that delivered three decades of rapid expansion but has run out of steam.
A development blueprint issued last month by the ruling party promises to revive economic growth by giving the free market a bigger role and opening more areas to private business. It promises to inject more competition into some industries dominated by state companies but says government ownership will remain the core of the economy.