The official SANA news agency quoted the bank as saying the pound was trading at 517.40 against the dollar on Sunday compared to 487.44 on Thursday, the last day of the Syrian working week.
On the black market the pound was trading at 550 against the dollar.
Economist Chadi Ahmad told AFP said the sharp drop in the exchange rate was due to growing demand by the government to use dollars to buy petroleum products overseas ahead of winter.
"The government is trying to acquire petrol because of the shortage in the markets, as well as diesel before the winter season," he said.
The value of the Syrian pound has depreciated by more than 110% to the dollar since Syria's conflict erupted in March 2011.
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At the time, the head of the central bank said Syria had reserves of some $18 billion, but experts say much of that has been used.
The World Bank said in April that these reserves had dropped to $700 million by the end of last year.
It said the "severe decline in oil receipts since the second half of 2012 and disruptions of trade due to the conflict" had put pressure on the exchange rate.
Falling export revenues and declining reserves had caused the currency's "significant depreciation", it added.
In May, the official exchange rate jumped by more than 20 percent to 620 pounds against the dollar overnight.
Oil production in Syria has dropped to 8,120 barrels per day compared to the 380,000 barrels produced daily before war broke out in 2011.
As well as devastating the economy, the conflict has killed more than 290,000 people and displaced millions.