According to police records, Garcia was found raped and strangled to death in a flowerbed near the Central Baptist Church on 18 Street in Lubbock.
Garcia's murder was considered a cold case until police arrested Albert Martinez on DNA evidence that linked him to the crime.
It's taken three years since to get the case to trial due to several delays.
The exact reason for why Martinez targeted Garcia is unknown, but court documents indicate Martinez did know Garcia' husband from prison.
Martinez could face life in prison.