The incumbent mayor, Charles Dail, stood for reelection to a second term.

In the primary election, Dail received a majority of the votes and was elected mayor outright with no need for a run-off.

On March 10, 1959, he came first in the primary election with 63.4 percent of the vote, more than 45 percent higher than James W. Morgan, his nearest competitor.

Because Dail received a majority of the vote, there was no need for a run-off election, and he was consequently re-elected to the office of the mayor.

[1] Because Dail received a majority of the vote in the primary, no run-off election was held.