The estimate by the Stockholm Environment Institute is based on the assumption that climate-altering carbon emissions continue their upward spiral without a pause.
Warmer seas will lead to greater acidification and oxygen loss, hitting fisheries and coral reefs, it warns.
Rising sea levels and storms will boost the risk of flood damage, especially around the coastlines of Africa and Asia, it adds.
On a business-as-usual scenario, Earth's global temperature will rise by some four degrees Celsius (7.2 degrees Fahrenheit) by century's end, says the report, "Valuing the Ocean."
On this basis, the cost in 2050 will be $428 billion annually, or 0.25 percent of global domestic product (GDP).
By 2100, it would rise to $1,979 billion, or 0.37 percent of output.
If emissions take a lower track, and warming is limited to 2.2 C (4 F), the cost in 2050 would be $105 billion, or 0.06 percent of worldwide GDP, rising to $612 billion, or 0.11 percent, by 2100.
"This is not a scaremongering forecast," says the report.
It cautions that these figures do not take into account the bill for small island states swamped by rising seas. Nor do they include the impact of warming on the ocean's basic processes, such as nutrient recycling, which are essential to life.
"The ocean has always been thought of as the epitome of unconquerable, inexhaustible vastness and variety, but this plenty more fish in the sea' image may be its worst enemy," notes the report.
"The immense scale of the ocean, and its remoteness from most of our daily lives, has contributed to its chronic neglect."