Tropical storm warnings remain for some of the state's islands, as the storm is due to progress west.
The state's governor says there "amazingly" does not seem to have been any loss of life besides a car crash.
The Caribbean country has been recovering since a tropical cyclone hit it last year.
The El Niño phenomenon is likely to be particularly intense this year, scientists warn. If so North America may face extreme weather, higher food prices and greater health risks.
These powerful tropical storms are generally becoming more intense as the world warms.
Norwich Jamaica Aid says sound systems and selectors will be performing to raise "vital funds".
The event in Penzance is in support of ShelterBox which is involved in recovery efforts.
A family in Jamaica are still battling the destruction caused by Hurricane Mellisa last month.
Aiesha Barrett's track Jamaica Strong has become an anthem for the hurricane-hit country.
