Judge Ahmad Zargar is named in the Consolidated List of Financial Sanctions Targets in the UK found on the Foreign and Commonwealth Office website.
Judge Zargar is due to hear the appeals of Pastor Yousef Nadarkhani (pictured below), Mohammadreza Omidi, Yasser Mossayebzadeh and Saheb Fadaie on Monday.
Christian Solidarity Worldwide's Chief Executive Mervyn Thomas said: "We hope the appeal court judge will rule in accordance with the law and overturn the original verdict in the interests of justice; however we have grave concerns about the judge who has been selected to hear the case."
The list names individuals and organisation subject to financial sanctions by the UK. Some are accused of aiding nuclear proliferation in Iran, while others are accused of human rights abuses. Judge Zargar has been on the list since April 2014.
The four men were each jailed in July for ten years after a Tehran judge found them guilty of "acting against national security" by "promoting Zionist Christianity". Pastor Nadarkhani and Mr Omidi also received additional two year sentences.
Mr Mossayebzadeh, Mr Fadaie and Mr Omidi are additionally awaiting the outcome of their appeal against a sentence of 80 lashes each that was handed down in 2016, following their convictions for drinking wine during a communion service.
According to the organisation Article 18, Judge Ahmadzadeh has previously sentenced at least 15 Christians to between five and 10 years in prison, with another receiving a 15 year sentence.
Mr Thomas, added: "The national security charges levelled against these men were spurious, and their sentences are excessive, amounting to a criminalisation of Christian practice."
"The international community must press the Government of Iran to uphold this constitutional obligation, and to respect the right of its citizens to the full enjoyment of freedom of religion or belief, as outlined in the International Covenant on Civil and Political Rights, to which it is signatory."
Christian Solidarity Worldwide is a Christian organisation which supports believers living under pressure because of their faith.
Top picture: Saheb Fadaie, Youcef Nadarkhani, Yasser Mossayebzadeh and Mohammad Reza Omidi.