South Korea's spy agency has said Kim Jong Un ordered Hyon Yong Chol be killed by firing squad after being caught napping.
It's claimed the minister was shot with anti-aircraft guns whilst hundreds watched on.
South Korea's NIS told reporters it was sure about its information but it has a history of being wrong on some occasions.
North Korea is a secretive, authoritarian state making the reports impossible to confirm or deny unless the minister appears in public.
Christian peer and chair of Parliament's All Party Group on North Korea, Lord Alton, told Premier's News Hour the report was horrifying.
"It's becoming more brutal and more and more unstable," he said, "the execution is designed to underline the absolute power of Kim Jong Un but what it does do is underline his absolute inhumanity."
The House of Lords member added: "All these signs of instability show a leader who is insecure but is also unstable as well.
"He was due last month to go to Moscow but instead he sent his Defence Minister.
"Now he's murdered his defence minister if these reports are true."
In 2013, Kim Jong Un had his uncle and chief deputy, Jang Song Thaek, executed for treason.