An Icelandic court found him guilty of market manipulation in the lead up to the 2008 financial crisis.
"This sentence is a big surprise to me as I did not nothing wrong," Sigurjon Arnason told Reuters.
The former chief executives of Iceland's two other big banks, Glitnir and Kaupthing, have already received jail sentences.
The three banks imploded in 2008 after acquiring assets worth approximately 10 times the size of Iceland's economy.
A Reykjavik court said that nine months of Mr Arnason's sentence would be suspended.
Two of his colleagues - Ivar Gudjonsson, a former director of proprietary trading, and Julius Heidarsson, a banker - were also convicted and sentenced to nine months in prison, of which six months would be suspended.
Unlike other Western countries, Iceland has pursued prison sentences for the chief executives and others who were involved in the 2008 financial crisis.
Hreidar Mar Sigurdsson, the former chief executive of Kaupthing - formerly Iceland's largest bank - received a jail sentence of five and a half years - the heaviest sentence for financial fraud in Iceland's history.
The country's former prime minister, Geir Haarde, was also found guilty of negligence leading up to the crisis but was not given a jail term.
Former Landsbanki boss Sigurjon Arnason has been sentenced to 12 months in prison.