Charles Kendrick, 25, from Carlisle, is serving a five year sentence after he was convicted of possession with intent to supply Class A drugs at Carlisle Crown Court in August 2015.
He absconded from the prison on Monday and is thought to be in the Cumbria area.
He is described as white, 6ft 2in tall and has a three inch scar on his left forearm.
Police are urging anyone who has seen Kendrick or anyone who has any information on his whereabouts to get in touch with us.
Anyone with information can contact police on 101 quoting log number 605 of July 17.
Police revealed they were searching for Kendrick less than an hour after they named another prisoner who had absconded from the open jail.
David McConnell, 34, from Liverpool who is serving a sentence of nine years and six months after he was convicted of drugs and burglary offences at Liverpool Crown Court in October 2014, absconded on July 11
Lee Leatherbarrow went missing from HMP Kirkham on the same day.
He was sentenced to five years in prison at Chester Crown Court in February 2016 for aggravated vehicle taking, conspiracy to commit burglary and conspiracy to steal a vehicle.
Also still missing is Dean Kerr, 29, formerly of Stonegarth, Carlisle, went missing from HMP Kirkham on Saturday.