Wolf has filed a Federal lawsuit in the Eastern District of Arkansas.
Tuesday, John Wolfe received forty-two percent of the votes on Democrat ballots.
President Obama received fifty-eight percent.
Even though Wolfe surpassed the 15 percent vote threshold to be eligible for delegates, the state Democratic Party has said it will not afford him any delegates.
The party has said Wolfe failed to meet a filing deadline and did not follow the party's requirement for delegate selection.
Wolfe says by taking his filing fee of $2,500, they waived opposition to his candidacy.
Arkansas has 55 delegates and three alternatives.
"The John Wolfe Campaign, which stands up for the average voter, will not let this injustice stand," said Elizabeth Wilson, campaign spokesperson.
"We will fight this injustice through the court system so that the 42 percent of Arkansans who supported John Wolfe will be heard at the national convention."
In addition to suing the Arkansas Democratic Party, Wolfe has vowed to sue the state party in Louisiana, which is also denying him the chance to win delegates.
Wolfe is heading for Texas where he will stump for votes there. The Lone Star state's primary election is the day after Memorial Day.