It lowered its benchmark rate by 25 basis points to 5.1%, saying the move was aimed at boosting development.
Last year's growth rate - 7.4% down from 7.7% in 2013 - was the weakest in 24 years.
The cut is the third in six months and will take effect from Monday.  It follows other measures designed to spur growth in China, including tax cuts.
China's slowdown is expected to continue for some years. Last week, the International Monetary Fund (IMF) predicted China's growth would stabilise at about 6% by 2017.
Also last week, weaker than expected official figures on both trade and inflation were released. The rate cut suggests data to be published this week, on industrial output and investment, may also disappoint.
The country's economic problems also include the property market, which is cooling after a damaging period that saw a speculative bubble emerge.
The central bank said in a statement: "China's economy is still facing relatively big downward pressure.
"At the same time, the overall level of domestic prices remains low, and real interest rates [interest rates relative to inflation] are still higher than the historical average."
Recent rate cuts have not yet fully filtered through to market rates.
Li Qilin, an economist at Minsheng Securities, said: "The effectiveness of the rate cut won't be very big.
"The PBOC has already cut benchmark interest rate by a total of 75 basis points, but borrowing costs have only fallen marginally."
One economist suggested Chinese interest rates have far further to fall.
Li Huiyong, an economist at Shenwan Hongyuan Securities, said: "This won't be the last cut. "The rate could be lowered to 2% at least, and we expect the economy to gradually stabilise in the coming two quarters."
China's central bank has cut interest rates for the second time this year, amid a continuing economic slowdown.