Viktor Orban, leader and prime ministerial candidate of Fidesz, cast his vote with his wife and their two oldest children in Budapest.
He told reporters: "I have brought two new voters which gives me confidence regarding the future. The biggest stake at today's election is defeating hopelessness."
Orban vowed to unleash the country's true potentials.
He said: "Over the past years Hungary has become a country which no longer believed it is capable of a better performance than what it actually showed."
The country's economy contracted by 6.3 per cent last year, while unemployment is running at 11.4 per cent - the highest since 1994 - which has further increased public discontent over the Socialist governments' spending cuts and tax hikes.
The Socialist government led by technocrat Gordon Bajnai had to make painful budget cuts to rein in the deficit under a financing deal led by the International Monetary Fund, which rescued Hungary from financial collapse in 2008.
The budget cuts have helped stabilise Hungary's finances and regain investors' confidence but exacerbated the recession.
Erzsebet Mesterhazy, 69, said, after casting her ballot: "My hopes are the same as those of many other people. Fidesz, Fidesz, Fidesz."
Another voter Gabor Kovats, 66, said: "I think jobs are the most important, but I am afraid that slogans will remain only slogans.”
Economists say Fidesz will need to implement deep reforms to reduce a bloated local government sector and make the health care and education systems more efficient to put Hungary back on a track of sustainable and strong economic growth.
Nationalist Jobbik, which has capitalised on public anger over economic hardship and a growing resentment towards a large Roma minority, may end up as the second biggest parliamentary force and some analysts said significant gains by Jobbik could cause unease among investors.
There are 386 seats in parliament, of which 176 seats are decided by majority vote in individual constituencies. A further 210 seats are allocated through regional party lists and a national compensation list.
In the first round, Hungarian voters are casting two ballots, one for an individual in their constituency and one for their party of preference tallied in the regional lists.
Polls opened at 0400 GMT and will close at 1700 GMT.
The first preliminary results are expected after 2000 GMT.