An elderly Queensland man who sent threatening letters and explosives to public figures, including the Prime Minister, has lost an appeal against his sentence.

In July, John Gilbert Gordon, 81, pleaded guilty in Brisbane's District Court to 11 counts relating to the unlawful use of the postal service.

Six of the letters contained bullets connected to a detonator - including one that was sent to Prime Minister Julia Gillard - which suggested all refugees would be shot.

Gordon admitted to posting anonymous letters to other public figures, including then Queensland premier Anna Bligh, Federal Opposition Leader Tony Abbott and then Catholic Archbishop of Brisbane, John Bathersby.

He was sentenced to two-and-a-half years in prison, to be released after eight months on a $500 good-behaviour bond.

The sentencing judge noted that although the language used in the letters might be discerned to be that of a crank, those who received them would have been afraid.

His lawyers appealed against the sentence on the basis that Gordon should not have been required to serve any time in custody due to his age, poor health and cooperation with authorities.

However, on Tuesday, the Court of Appeal dismissed his appeal.

The court found Gordon might have been required to serve 10 months in custody instead of the eight months stipulated.

One-third of the maximum prison sentence is usually required to be served in Queensland when taking into account a timely plea of guilty, good character and other mitigating circumstances.

AFP investigation

In several letters Gordon asserted the Vatican would be destroyed, and in another he claimed to have poisoned the water supply of a motel he believed was housing asylum seekers.

That letter, mailed to a Brisbane motelier in May 2010, stated: "Any motel in Australia who houses [asylum seekers], will bear the bombs and as a result pieces of your motels will land in Canberra."

Two months later, a letter posted to Tony Abbott lead to an investigation by the Australian Federal Police (AFP).

It stated: "We have just successfully injected a deadly poison into the water supply of the motel at Boondall … We will wipe all foreigners of [sic] Australian Soil real soon."

Forensic examination of that letter revealed an imprint of his name from other correspondence written on the same notepad.

A 14-month investigation by the AFP culminated in a search of Gordon's Caboolture home, and his arrest.

The officers discovered a large quantity of ammunition, including 0.22 calibre cartridges and detonators, which were the same as those used in the letters.

They also seized documents containing samples of Gordon's handwriting, along with eight firearms and two silencers from his bedroom.

Gordon also sent letters to the Reserve Bank governor, and the chief executive officers of the Westpac and Commonwealth banks.