Asia Bibi became the first woman in the country to be sentenced to death for blasphemy after a row with labourers on the farm where she worked.
She will be sentenced in October.
Her Muslim co-workers refused to drink water she had brought for them because as a Christian they considered her to be unclean.
Christian charity Release International is now urging the Pakistani government to change its laws.
Blasphemy against Islam is punishable by guest in the Muslim nation.
For the last five years there has been a put on Asia Bibi's head and her family have been forced into hiding.
Release International is asking the government to acquit Asia Bibi and repeal its strict blasphemy law, which is open to abuse.
It has launched a petition asking Pakistan's Prime Minister Nawaz Sharif to put a stop to her trial.
Release International Chief Executive, Paul Robinson, said: "We call on the government of Pakistan to abolish the blasphemy laws and seek to create a society where every Pakistani citizen is free to exercise their faith and live in peace with their neighbours."
He went on: "It [Pakistan] must review every blasphemy case and repeal these notorious laws which target Christians and other minorities and are often invoked to whip up violent persecution."
Asia has faced threats despite being in prison and one cleric is alleged to have offered around £4,000 for whoever kills her.
Politicians have also been in danger for opposing the strict laws.
In 2011, Punjab governor Salman Taseer was murdered by his own bodyguard for calling for Asia's release.
The minorities minister, Shahbaz Bhatti, a Christian, was also assassinated later in the same year.
If Supreme Court uphold the sentence, Asia Bibi would become the first woman in Pakistan to be executed for blasphemy.
Andrew Boyd from Release International told Premier's News Hour even if she survivors people will want her dead.
He said: "We have a person here who's been on death row now for six years.
"There's been a price put on her head - a reward of £4,000 has be given for her death.
"Her family have been forced into hiding, and what did she do, she brought somebody a cup of water."
Andrew Boyd went on: "Her family have had to go into hiding - but this is fairly common, I've been out to a village in Pakistan where a cry of blasphemy was broadcast from a mosque loud speakers - and a mob descended on that village and set fire to it.
"They killed a family of seven.
"They burnt them to death in a house."
He said that it is hard fight these cases as an accusations is enough for someone to get killed: "Not even an offence, but just a perceived offence, the nearest hint that anybody has done anything, like abuse a page of the Koran for example.
"The moment anybody accuses somebody of blasphemy in Pakistan, there is a mob there willing to take them out."
Andrew Boyd told Premier there have been 50 cases since 1990 when vigilantes have murdered those accused of blasphemy.
Listen to Premier's Alex Williams speak to Andrew Boyd here:
