Nazanin Zaghari-Ratcliffe - a charity worker accused of security offences - was detained while trying to leave the country with her baby daughter after visiting relatives in April 2016.
Her family denies she broke any laws.
Her husband, Richard Ratcliffe, who is from London, said his wife's detention was a "stain" on Iran.
Mrs Zaghari-Ratcliffe, 38, who works for the charity the Thomson Reuters Foundation, has been detained in Iran since her arrest last year.
The couple's two-year-old daughter has remained in Iran after the government confiscated her passport, and is being looked after by her grandparents.
Mrs Zaghari-Ratcliffe's family said in September that a Revolutionary Court had handed down the five-year term.
She was accused of allegedly plotting to topple the government in Tehran, but the official charges against her were not made public.
According to Mr Ratcliffe, his wife's appeal was dismissed in a secret hearing of an Iranian Revolutionary Court on 4 January but only announced on 22 January.
In a statement, her husband said the precise charges against her remain secret, but that two new accusations were made at her appeal.
One was that she had been head of recruitment for the BBC's Farsi service when it was launched in 2009. Her family say she worked on a BBC training project for youth in Afghanistan and Iran, but never worked for BBC Farsi.
The other charge was that she was married to a British spy. Mr Ratcliffe is an accountant.
Monique Villa, chief executive of Thomson Reuters Foundation said she is "outraged by this new mockery of justice", and reiterated Mrs Zaghari-Ratcliffe never worked for BBC Farsi and that her husband "is not a spy but a reputable accountant".
"I am fully convinced of Nazanin's innocence," she added.
Francesca Unsworth, BBC World Service Group director, said Mrs Zaghari-Ratcliffe had briefly worked for charity BBC Media Action in a "junior administrative capacity" but had never worked for BBC Persian.
"In any case, to suggest that being employed by BBC Persian is tantamount to 'acting against national security' is patently ludicrous," Ms Unsworth added.
Mr Ratcliffe said: "The lack of justice in Nazanin's case continues to be a stain on Iran. The continued attempt to frame Nazanin behind secrets and lies brings shame.
"It is a needless waste of a mother and child's life for their own political bargains and economic interests."
Iran does not recognize dual nationalities, meaning those detained cannot receive consular assistance.
Since her imprisonment, her family have campaigned on her behalf, highlighting her deteriorating health while in jail and her anguish at her separation from her daughter.
A court in Iran has rejected an appeal against a five-year prison sentence given to a woman with dual British and Iranian citizenship.