The vote was prompted by corruption allegations against Prime Minister Ehud Olmert, the current party leader. Olmert announced on July 30 he will step down once a new party leader is in place, though he is set to stay on as a caretaker prime minister until a new coalition government is formed.
Kadima is expected to announce the victor on Thursday, if the winner received the required 40 percent majority of the vote. If not, a run-off will be held Sept. 24.
Livni, who could be the country's first female prime minister in more than 30 years, has said she wants to form a new government coalition without holding early elections and plans to re-energize peace negotiations with Palestinians, according to the New York Times.
Livni's nickname is "Mrs. Clean," and she has been able to stay removed from corruption allegations against other party members. She is known for being a soft-spoken negotiator and has played a key role in past negotiations with the Palestinians.
"You can determine today what the character of Kadima will be," said Livni, after casting her vote in Tel Aviv, the Associated Press reported. "You can determine today if you really have had enough of old-time politics. Come and vote, bring your children, and show them how you are changing the country."
Transportation Minister and former Gen. Shaul Mofaz is Livni's main competition. He claims that his own polling shows him in the lead, reported the New York Times.
"I stand behind my belief that I am going to win," he said after voting near Tel Aviv, Agence France-Presse reported.
Mofaz is described by many as hawkish and is likely to attract votes from party members who favor giving the Palestinians fewer concessions. In August, he warned that Israel would take military action against Iran if the world can't curb its nuclear ambitions.
The next prime minister will also be charged with determining the direction of peace talks with the Palestinians, as well as responding to Iran's nuclear aspirations and shaping a relationship with Syria.
Kadima's new leader has a good chance of becoming the next prime minister, but new elections could mean another party's leader might succeed Olmert.
Kadima is the largest party in a four-member governing coalition that is in a weakened state. The new leader would need to pull together a new parliamentary alliance in six weeks, reported CBS. Otherwise, national elections would be held in early 2009, a year and half ahead of schedule.
The Labor Party, which holds the most parliamentary seats among the Kadima coalition partners, may pull out, which could force an election. New elections could feature several contenders for the role of prime minister, including former Prime Minister Ehud Barak, who heads the Labor Party, or former Prime Minister Benjamin Netanyahu, head of the opposition Likud Party.
Despite the implications of Wednesday's vote, interest has been tempered. Kadima has 73,000 eligible members and about 60 percent of eligible voters are predicted to turn out.