The victim has been named as Lawrence.
His family say his throat had been slit during the attack.
Detective Chief Inspector Geoffrey Boyce said: “Police were called to the scene after the body of 56 year old Laurence Shaw was discovered inside his home in Hillmount Gardens at around 1.30pm yesterday afternoon, Monday 9th October.
“A post mortem examination will be carried out in due course to determine the cause of death.
“A 39 year old man was arrested during the early hours of this morning on suspicion of murder and remains in police custody at this time.”
Detective Chief Inspector Boyce continued: “I am appealing to anyone who noticed any suspicious activity in the Hillmount Gardens area since Saturday afternoon, or anyone who has any information that can assist us with our enquiries, to contact detectives in Larne on 101 quoting reference number 687 09/10/17.
“I am particularly keen to speak with anyone who saw or spoke with Laurence at any time over the weekend, or anyone who was in his company.
“Information can also be given anonymously through the independent charity Crimestoppers on 0800 555 111.”