UK-based Chatham House says more needs to be done to protect key transport routes such as the Panama Canal, the Suez Canal and the Turkish Straits.
Almost 25% of the world's food is traded on international markets.
This, the report says, makes food supply and prices vulnerable to unforeseen crises or climate change.
Infrastructure at the chokepoints is often old and would struggle to cope with natural disasters which are expected to grow in frequency as the planet warms, the report authors add.
They urge governments to invest in "climate-resilient" infrastructure, and diversify food production and stocks.
The report gives examples of how reliant the world is on this trade:
"The risks are growing as we all trade more with each other and as climate change takes hold," says Laura Wellesley, one of the study's authors.
There are risks for both the food security of importing countries and the economies of those exporting food, she added.
The world's food security is increasingly reliant on 14 "chokepoints" for trade, a think-tank report has warned.