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.
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