Incumbent Prime Minister Portia Simpson Miller, 70, is being challenged by the Jamaica Labour Party under Andrew Holness, 43, which is promising tax cuts and new jobs.
Austerity measures introduced by Ms Simpson Miller have led to growth.
Inflation fell to a 48-year low during her time in office.
Last year GDP grew by 1.3%, according to World Bank figures.
But with youth unemployment at 38%, Mr Holness' plan to increase spending to boost jobs has attracted voters.
Mr Holness says he wants to turn Jamaica into "the Silicon Valley of the Caribbean".
In 2013, the country agreed to a four-year International Monetary Fund (IMF) loan package in exchange for swapping its debt.
Ms Simpson Miller's party, the People's National Party (PNP), prides itself on "bringing back the country from the verge of economic collapse" but the package expires next year.
The final days of campaigning were marred by violent incidents.
Two people were shot dead and several more injured during a campaign event on 7 February as Mr Holness was addressing supporters.
On Tuesday, shots were also fired during a PNP rally triggering a stampede in which dozens of people were hurt.
However, the numbers of those hurt or killed have been much lower than in previous election campaigns.
Sixty-three parliamentary seats are up for election.
The party that wins a majority of those seats will form the government for a five-year term.
There are 1.8 million registered voters.
Members of the police and military as well as election workers cast their votes earlier, on Monday.
The people of Jamaica are voting in a closely contested general election after a campaign dominated by economic issues in the heavily indebted nation.