* Former ultra-nationalist bidding to become PM
* Centre-right promising economic overhaul
* Serbia setting out on talks on joining EU (Adds opposition leader, detail on results)
By Ivana Sekularac and Matt Robinson
BELGRADE, March 16 (Reuters) - Serbia's centre-right Progressive Party attempted to cement its grip on power for the next four years in a snap election on Sunday, promising an economic overhaul of the ex-Yugoslav republic as it embarks on talks to join the European Union.
Opinion polls suggest the party may win more than 40 percent of the vote, a haul unprecedented in the almost 14 years since Serbia came in from the cold with the ouster of strongman Slobodan Milosevic.
Party leader Aleksandar Vucic, 44, a former ultra-nationalist and once feared Milosevic-era minister who converted to the pro-EU cause in 2008, is likely to become prime minister.
The Progressive Party (SNS) forced the snap election after just 18 months in coalition government, saying it needed a stronger mandate to overhaul Serbia's shaky finances.
The party's domination owes much to Vucic's personal popularity as the face of a popular anti-crime crusade that saw Balkan retail tycoon Miroslav Miskovic put on trial.
The campaign has struck a chord with many Serbs angry at decades of deep-rooted graft.
Critics, however, are unnerved at the power amassed by a man who up until five years ago was a virulent anti-Western disciple of the Greater Serbia ideology that fuelled the wars of Yugoslavia's bloody demise in the 1990s.
Vucic now says Serbia must follow fellow ex-Yugoslav republics Slovenia and Croatia into the EU, and is advocating root-and-branch reform of the bloated public sector, pension system and labour legislation.
"I expect reforms, job creation and the fight against corruption to be the main issues for us after the election," Vucic said as he voted among the high-rise apartment blocks of New Belgrade shortly after polls opened at 7 a.m. (0600 GMT).
The country of 7.3 million people must commit to rein in its budget deficit and public debt in order to secure a new precautionary loan deal with the International Monetary Fund, which could come soon after a new government is formed.
Timothy Ash, head of emerging markets research at Standard Bank, said Serbia had the potential to become an "IMF poster child".
"The political establishment and the population appear ready/primed for reform, and a new strong government with a fresh mandate has no excuse now for not reforming," he said.
The opposition is warning voters against handing too much power to Vucic. He was information minister in the late 1990s when newspapers were fined and shuttered under a draconian law designed to muzzle dissent as Milosevic led Serbia into war with NATO over Kosovo.
The outgoing government, in which Vucic was deputy prime minister, went a long way to finally putting to rest the issue of Kosovo. It agreed to cede Serbia's last foothold in its former southern province, which declared independence six years ago and has been recognised by more than 100 countries.
In return, the EU granted Serbia membership talks, which formally began in January shortly before the government fell.
The process, likely to run beyond 2020, should help steer reform and lure much-needed foreign investment to the biggest market to emerge from the ashes of Yugoslavia. Serbia is a natural hub for a region with deep linguistic and cultural ties.
"I voted for Vucic because he's doing the right thing," said 68-year-old pensioner Ceda Kerkez after voting in the capital. "He's not in bed with the tycoons, he's arresting the tycoons, and I think there will be more arrests after the election."
Vucic's SNS is expected to bring several other parties into government, possibly to share the blame for what promises to be a painful economic overhaul. The outgoing government ducked most tough economic measures.
The Socialists of outgoing Prime Minister Ivica Dacic and the Democratic Party of former Belgrade mayor Dragan Djilas are fighting it out for second place, a long way behind the SNS.
"They (SNS) promised much, but did not fulfil any of their promises," said voter Mirjana Jelovic, a 69-year-old retired doctor. "That's why I voted for the Democratic Party."
Djilas told reporters in Belgrade on Sunday the SNS was offering empty promises and "fairytales about investment".
"Another year of this and Serbia will be bankrupt," he said.
Polls close at 8 p.m. (1900 GMT) and unofficial results are expected by around 10 p.m. (2100 GMT). (Writing by Matt Robinson; Editing by Sophie Hares)