Henry W. Glover was born around 1837 in Georgia. By the early 1860s, he was working as a farmer in Alabama.
He enlisted in the Confederate army on July 3, 1861, and he mustered in as a private in Company B of the 15th Alabama Infantry. The regiment took part in the Second Battle of Manassas, the Battle of Antietam, the Battle of Fredericksburg, the Battle of Gettysburg, the Battle of Chickamauga, the Overland Campaign, and the siege of Petersburg.
He was wounded in the Battle of the Wilderness, but he eventually recovered and rejoined the regiment. He eventually earned a promotion to 2nd lieutenant, and he was promoted to 1st lieutenant on August 15, 1863. He was wounded in the head in the Battle of Darbytown Road on October 13, 1864, and he died in Richmond, Virginia, on October 19, 1864.