Charles Evenson was Esme Cullen's first husband. They married when she was still human. He was born in the late 1800's. His abusive personality drove Esme away when she got pregnant, and in 1926, he was murdered by Edward Cullen.
Biography
Charles was a violently unpredictable man and a very abusive husband, but his gentle exterior covered this personality from the public. He was drafted as a soldier in World War I, only to return in 1918, much to his wife's dismay. She left him in 1920 after discovering she was pregnant, not wanting her child to be raised by him. Presumably, Charles never knew of his son's existence, nor of his death shortly after birth. Also then, he most likely never knew about his wife's suicide attempt, nor her subsequent change into a vampire by the one who would later become her second husband, Carlisle Cullen.
When Edward Cullen went astray to lead a nomadic lifestyle, he dedicated himself to only killing evil doers, thinking that it wouldn't matter as long as justice was served: Charles was his first victim.
Note
His existence is only mentioned in The Twilight Saga: The Official Illustrated Guide.