Christiane Berthiaume, spokeswoman for the UN agency, on Tuesday said the attacks on several convoys took place in recent weeks in zones controlled by Darfur's rebels.
"The roads are dangerous. Every day, trucks get attacked, their cargoes are stolen and their drivers are kidnapped," Berthiaume told journalists.
Security problems are putting the WFP's operations in Darfur at risk, she added.
Some 2.7 million people in the region rely on food aid from the WFP, and the agency is finding it increasingly difficult to recruit drivers because of the violence.
That is raising fears that it will be unable to deliver enough supplies before the rainy season starts in April, turning the region's roads into a quagmire, Berthiaume said.
Despite pressing Sudan's governments and Darfur's rebels, the WFP has received no guarantees that its convoys will be safe, she said.
Sudanese authorities blamed the abduction on the rebels.
The Darfur conflict broke out in February 2003.
It pits rebel groups who are campaigning for a greater share of the power and wealth of Sudan against the Khartoum government and its affiliated militias.
Fighting and the humanitarian crisis in the region has claimed between 180,000 and 300,000 lives, and displaced more than two million people.