Its leader, Gabor Vona, often works shifts in minimum wage jobs - a waiter, a construction worker - to show he is in touch with ordinary peoples' concerns.
A senior party figure in 2012 proposed drawing up lists of Jews in parliament, though he later apologised and said he was misunderstood.
"Jobbik is continuously ...increasing its popularity," Vona told party supporters late on Sunday. "And ahead of the European Parliament elections it is important to make clear that today in the EU Jobbik is the strongest national radical party."
In the past four years, Orban's policies have included a nationalisation of private pension funds, swingeing "crisis taxes" on big business, and a relief scheme for mortgage holders for which the banks, mostly foreign-owned, had to pay.
Orban has pledged more of the same if re-elected, and the business community expects him in particular to press ahead with a plan to transfer big chunks of the banking sector into Hungarian hands, and impose more levies on foreign power firms.
More unpredictable policies could weigh on Hungary's forint currency, especially if the central bank - led by a close ally of Orban's - cuts interest rates further from record lows, against a backdrop of jittery sentiment in global markets.
His policies have played well with voters and helped Hungary emerge from recession, but some economists say that by hurting foreign investors, Orban may have scared off the kind of investment Hungary needs for long-term growth.
"Big business do not want the frequent changes of policy, particularly in terms of taxes, which were characteristic of Orban's last term," said Timothy Ash of Standard Bank.
The election was a new low point forthe leftists, who were ousted in 2010 after racking up huge amounts of public debt, and after their leader four years earlier was caught on tape admitting his government was lying to the public.
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Some Hungarians worry that, without a credible challenge to his dominance, Orban has accumulated too much power.
Socialist leader Attila Mesterhazy acknowledged defeat but declined to congratulate Orban, saying the prime minister had won unfairly by changing the election system to Fidesz's advantage and compromising media freedom - allegations the government denies.
Mesterhazy also lamented the strong performance by the Jobbik, calling it a party that "is poisoning the whole of Hungarian society."