In 1973, Gary McCool, from the Bogside, was sentenced to 12 years after he and another man were detained close to a car the weapons were found a year earlier.
Mr McCool, who was 18 when he was arrested, has always denied involvement and is believed to be only one of two men allowed to examine his own files by Forensic Services Northern Ireland.
He had asked the CCRC to re-examine his case in 2016 after a previous attempt to have it referred to the Court of Appeal failed.
The new review comes after a report produced by English experts raised concerns about the forensic evidence used to convict him.
A forensic expert says that in his opinion the comparison of fibres was “deficient, both by modern standards and given the methods available at the time”.
He also said that the actions of British soldiers and RUC officers during the detention of Mr McCool “contravened many of the now routine anti-contamination measures”.
Mr McCool said his arrest 40 years ago had a huge impact on his family.
“Immediately after I was arrested both parents developed serious illnesses, my mother developed cancer and my father had a heart attack,” he told The Irish News.
“I feel sad about that, maybe they paid more of a price than I did.”
He also said his own life had been impacted as a result of his detention. When arrested he said he worked as an electrical engineer and owned a car. He studied for a degree and a masters degree on his release but could not get a job because he was unable to get security clearance.
He said however he remains hopeful his case will be successful.
”I would like them (CCRC) to refer it to the Court of Appeal and have the conviction overturned and bring a bit of closure to the whole thing,” he said.
His solicitor Aiden Carlin has described his client’s case “a serious miscarriage of justice that needs to be referred back to the Court of Appeal immediately.”
A spokesman for the CCRC confirmed it is reviewing the case.
A spokesman for the Department of Justice told the newspaper: “This matter is the subject of an on-going review. It would not be appropriate for anyone to comment until the findings have been made public.”
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