When Galloway was 18 he was jailed for 10 years, with a minimum non-parole period of five years, for the fatal bashing of Richard Milton Jones on April 29, 2009.
Mr Jones, 64, an occasional small-time cannabis dealer who dressed as a woman and was known as "Diksy", suffered a savage and sustained attack at the hands of Galloway and Phillip Christopher Sanders, 42, in his Upper Hutt flat.
Three Court of Appeal judges later reduced Galloway's jail term to nine years, and cut his minimum non-parole period to four years.
After his arrest Galloway told police that he followed Sanders to the flat "to beat up a transvestite", that he "believed in Adam and Eve, not Adam and Steve", and that he did not deserve to live.
The court heard at the time that Galloway was highly intoxicated when he attacked Jones, had no hate crime history, was sexually abused as a child and had acted properly around a transvestite in prison.
Galloway and Sanders each blamed the other for the many serious injuries - including more than a dozen blows to the head - which resulted in Jones' death.
If you know where Galloway is or see him, call 111 immediately. To pass information to the police anonymously, call Crimestoppers on 0800 555 111.