Gail Cochrane, 53, had kept the gun for 29 years following the death of her father, who had been in the Royal Navy.
Police found the weapon, a Browning self-loading pistol, during a search of her home in Dundee while looking for her son.
She admitted illegal possession of the firearm, an offence with a minimum five-year jail term under Scots law.
Cochrane told the High Court in Edinburgh that she had never contemplated she might be committing a crime by keeping the gun or that she might need to get a licence for the weapon.
She said: "I thought it was just a war trophy."
Defence solicitor advocate Jack Brown argued that the circumstances surrounding the case were exceptional and that it would be "draconian, unjust and disproportionate" to jail the grandmother-of-six.
Prohibited weapon
However, Judge Lady Smith said: "I am not satisfied that a reasonable explanation has been put forward for not handing this gun into the authorities throughout the 29-year period she says she has had it in her possession."
The judge said she was unable to find herself satisfied that this was one of the rare cases in which exceptional circumstances existed.
She said: "The result is I have no alternative but to sentence Mrs Cochrane to a period of five years."
The case began after police arrived at the 53-year-old's home on 17 June 2009 with an arrest warrant for her son who had failed to turn up for a court appearance.
He was not at the flat, but the 80-year-old pistol was found underneath a mattress in her bedroom.
When interviewed, Cochrane told police that the gun had previously belonged to her father and that she had kept it when he died.
She said she believed it was a real gun, but had no ammunition for it.
The weapon was sent for examination by firearms experts who concluded that it was a Czech-made pistol dating back to about 1927.
Cochrane admitted having the 7.65 millimetre Browning self-loading pistol at her home without a firearms certificate and possessing the prohibited weapon without the authority of the Secretary of State or Scottish ministers.
