Abdul Rahman is charged with rejecting Islam and could face the death sentence under Sharia law unless he recants.
He converted 16 years ago as an aid worker helping refugees in Pakistan. His estranged family denounced him in a custody dispute over his two children.
It is thought to be Afghanistan's first such trial, reflecting tensions between conservative clerics and reformists.
Conservatives still dominate the Afghan judiciary four years after the Taleban were overthrown.
The BBC's Mike Donkin in Kabul says reformists, like the government under President Hamid Karzai, want a more liberal, secular legal system but under the present constitution it is hard for them to intervene.
Afghanistan's post-Taleban constitution is based on Sharia law, and prosecutors in the case says this means Abdul Rahman, whose trial began last Thursday, should be put to death.
When he was arrested last month he was found to be carrying a bible and charged with rejecting Islam which is punishable by death in Afghanistan.
Trial judge Ansarullah Mawlazezadah told the BBC that Mr Rahman, 41, would be asked to reconsider his conversion, which he made while working for a Christian aid group in Pakistan.
"We will invite him again because the religion of Islam is one of tolerance. We will ask him if he has changed his mind. If so we will forgive him," the judge told the BBC on Monday.
But if he refused to reconvert, then his mental state would be considered first before he was dealt with under Sharia law, the judge added.
He said he expected the case to take about two months to be heard.
The Afghan Human Rights Commission has called for a better balance in the judiciary, with fewer judges advocating Sharia law and more judges with a wider legal background.
Several journalists have been prosecuted under blasphemy laws in post-Taleban Afghanistan.
The editor of a women's rights magazine was convicted of insulting Islam and sentenced to death last year - but was later released after an apology and heavy international pressure.
Mr Karzai's office says the president will not intervene in the case.
Observers say executing a converted Christian would be a significant precedent as a conservative interpretation of Sharia law in Afghanistan.
But it would also outrage Western nations which put Mr Karzai in power and are pouring billions of dollars into supporting the country.