Nazanin Zaghari-Ratcliffe was sentenced to five years for allegedly plotting to topple the government in Tehran.
Her husband, Richard Ratcliffe, has criticised the UK government for a lack of action and said the appeal against the term was happening in "secret".
It is understood it is being held in Tehran on Wednesday.
Mrs Zaghari-Ratcliffe, 38 has spent time in solitary confinement since her arrest at Tehran Airport last April, with her two-year-old daughter Gabriella.
The child has remained in Iran after the government confiscated her passport and is being looked after by her grandparents.
Mrs Zaghari-Ratcliffe was sentenced to five years in jail in September on charges that have not been disclosed.
Mr Ratcliffe said the family could not go to his wife's appeal hearing and did not know when to expect a result as it was "another of these secret trials".
He said: "Obviously her father is terrified, as am I. We are increasingly on tenterhooks as to what could happen."
Mr Ratcliffe, 41, believes his wife is being used as a bargaining chip in a diplomatic row between Iran and the UK.
He said he will know when the appeal has happened and what was said in the courtroom but the final outcome "might come today, it might come next week".
There was a gap of about four weeks between his wife's trial and the verdict, he added.
Mr Ratcliffe said his wife had felt suicidal and had started a hunger strike during her time in jail but there was "more fight in her" since being moved out of solitary confinement over Christmas.
He told BBC Breakfast the outcome of the appeal was "unpredictable" as it could see her sentence quashed, reduced or increased.
Speaking about his daughter, Mr Ratcliffe said: "I have watched her grow up on Skype.
"She has lost her English, and she is now pretty much fluent in Farsi - with only a few words in English.
"Conversations now either have to be translated through one of her aunts and uncles or they are very physical - so playing peekaboo and watching her dancing."
Mr Ratcliffe said he was trying to get a visa so he could visit his wife and daughter.
Amnesty International UK said Mrs Zaghari-Ratcliffe was a "prisoner of conscience" who was being held for "peacefully exercising her right to freedom of expression and association".
Risk campaign manager Kathy Voss added: "Though she shouldn't even find herself in this awful position, we very much hope the appeal will rule in Nazanin's favour and order her immediate release."
The husband of a British-Iranian charity worker jailed in Iran is "terrified" about the outcome of his wife's appeal, he has said.