Bishop Jean Gilson-Levi of the Restored Covenant Churches of God has admitted illegally owning a shotgun.
Kent Online has reported that the man had declared the 16 gauge gun and ammunition when he travelled from his native Belgium "to do some hunting".
The 52-year-old, of Penfold Road, Folkestone, was returning to the UK last August when he was stopped and arrested for possessing a Special C16 semi-automatic without a certificate.
He pleaded guilty to two charges at Canterbury Crown Court.
Guy Wyatt, his lawyer, has asked for sentence to be postponed due to his ill health, telling Judge Adele Williams: "The defendant is significantly unwell. He had a heart attack five weeks ago."
It has been reported that before going to court the church leader had been to hospital for high blood pressure.
Judge Williams adjourned the hearing for three weeks and asked for an up-to-date medical report.
His lawyer told the judge that he had declared the firearm to the shipping company coming to the UK, "but when he declared it on the way out, shipping company staff referred him to the Border Agency."
Gilson-Levi is a Belgian-born missionary and founder of the Restored Covenant Churches of God, a Pentecostal apostolic organisation.
He was a comedian before he decided to pursue his life in the Church.