He enlisted in Tom Green's brigade of Cavalry in the Confederate States Army in the spring of 1864 and served until the close of the Civil War.

After a few years of practice, Kleberg was appointed as prosecuting attorney of De Witt County 1876-1890.

Kleberg was elected as a Democrat to the Fifty-fourth Congress to fill the vacancy caused by the death of William H. Crain.

He was reelected to the Fifty-fifth, Fifty-sixth, and Fifty-seventh Congresses and served from April 7, 1896, to March 3, 1903.

This article incorporates public domain material from the Biographical Directory of the United States Congress