Frederick Alexander was either born around 1813 or 1828 in Albemarle County, Virginia. His mother's name was Rebecca, and he grew up in Warren County, Mississippi. By the early 1860s, he was working as a laborer, although it is unclear whether or not he was enslaved. He enlisted in the Union army on July 27, 1863, in Natchez, Mississippi, and he mustered in as a private in Company I of the 5th USCT Heavy Artillery on August 7. According to his service record, Alexander was 5 feet, 5 inches tall, with black hair and eyes and a yellow complexion. He worked as a cook during his service. Alexander's regiment participated in multiple expeditions throughout the war, traveling to towns like Rodney, Fayette, and Yazoo City in Mississippi. The regiment, however, spent most of its time on garrison duty in Vicksburg, Mississippi. By the end of the war, the 5th USCT Heavy Artillery suffered heavy casualties, especially for a unit not engaged in any direct military combat, with almost 700 men dying from disease. Nonetheless, Alexander survived and even achieved the rank of corporal by the time the unit mustered out on May 20, 1866.

He lived in Vicksburg after the war. He married a woman named Lydia, and they had a son named Prince. On December 14, 1868, he applied for a Freedman's Bank account. He listed his occupation as farmer, and he reported that he worked for himself. He died sometime after 1870.