"We were alerted that a boat had sunk and that there are bodies on the beach in Khoms," 120 kilometres (75 miles) east of Tripoli, Red Crescent spokesman Mohammad al-Misrati told AFP.
"We don't know how many people were on board, but the coastguard has begun a rescue operation and we are preparing to retrieve at least seven bodies that have been washed up," Misrati added.
The latest sinking comes just days after a boat carrying nearly 400 would-be migrants foundered near Libya's western port of Zuwara.
"There are still 50 to 60 people who are missing," he said.
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Libya, with a coastline of 1,770 kilometres (more than 1,000 miles), has for years been a stepping stone for Africans seeking a better life in Europe.
Most head for Italy's Lampedusa island which is 300 kilometres from Libya.
People smugglers have taken advantage of chaos in Libya since the 2011 uprising that toppled and killed veteran dictator Moamer Kadhafi to step up their lucrative business.
In exchange for steep fees, they take would-be migrants on board rickety boats for the treacherous Mediterranean crossing.