The election was called after the recent collapse of Croatia's five-month old government.
This came after weeks of coalition infighting, warnings about creeping right-wing nationalism and a wave of public anger over ministerial conflicts of interest.
The 46-year-old MEP currently chairs Parliament's delegation to the EU-Ukraine parliamentary association committee and is a Vice-Chair of the foreign affairs committee. He is a member of the centre right EPP group.
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As newly elected President of the HDZ, Croatia's largest centre-right party, he said he has big plans for his party and for his country.
Plenković, a former diplomat, was recently named as the fifth head of the party founded by Franjo Tuđman, Croatia's first President, who led the conservative HDZ until his death in 1999.
The party's image has been hit by recent media reports questioning the transparency of the party's financial deals with several companies.
Plenković faces a challenge to significantly improve the HDZ's image ahead of the election, after support for the party fell to a record low of 21.5 per cent, according to an opinion poll published earlier this month.
The HDZ's traditional rival, the centre-left Social Democratic Party, SDP is well up on that figure, with 30.9 per cent of the votes, according to the same poll.
Plenković has called for his party to offer a policy platform "devoid of extremes and populism".
He said: "Croatia needs a new approach, a modern political platform and a strategic U-turn."
Described as an economic liberal, the MEP led Croatia's accession negotiations with the European Union, which the Balkan country joined in 2013.
He told the Financial Times, "This is a challenging time for the HDZ, Croatia, Europe and the world. We need a new vision and approach, which requires bold leadership and specific knowledge.
"We will revitalise the party," he said.
Plenković admitted mistakes in the HDZ's work in the past and said they needed to be corrected. "The solution can't be a policy that separates, which is based on ideological differences.
"Croatia needs a modern political platform."
He said, "I will insist that the HDZ strengthen the independence of all political institutions," he explained. "I want the HDZ to generate political stability."