The projection is lower than the 7.8 per cent expansion the country recorded in 2012, which was its weakest in 13 years, and comes as a slew of data indicate the economy is struggling to pick up pace.
"The main risk related to China remains the possibility that high investment rates prove unsustainable, provoking a disorderly unwinding and sharp economic slowdown," the World Bank said.
It tipped growth to pick up to around eight per cent next year and in 2015 -- unchanged from the bank's pervious forecast -- as "global conditions improve".
While the headline inflation rate is mild, price pressures remain in certain rapidly growing segments of the economy, including real estate, it added.
"Ensuring strong and stable consumption through raising household incomes to sustain growth is a priority in China," it said, adding more investment should be directed into agriculture, human capital and services and increased efficiency of investment.
The government should also try to reduce non-performing assets at Chinese banks, most of which are state-owned, that have piled up "during years of investment-led growth".
Other recent indicators have raised alarm bells, with exports showing almost no growth last month, while industrial output expanded at a slightly slower pace than April and big ticket investment growth also eased.
A survey by British banking giant HSBC showed China's manufacturing activity measured 49.2 in May, an eight-month low, and below the 50 mark that indicates contraction.
The World Bank's forecast cuts followed a recent lowering by the International Monetary Fund to 7.75 per cent from the previous 8.0 per cent.