The wife and mother of five has been on death row for more than four years, and detained for more than five years.
She appealed her death sentence to Lahore High Court, but it was upheld.
The Supreme Court is the final court of appeal in Pakistan, except for a pardon from the government itself.
According to The Guardian newspaper, Asia Bibi's lawyer Saiful Malook said: "On behalf of Asia Bibi I have today filed an appeal in the supreme court.
"We expect an early hearing of the appeal and hope that the proceedings will be over in one year."
Asia's husband, Ashiq Masih, has written a public letter to the President of Pakistan, Mamnoon Hussain, asking for his wife to be pardoned.
It says: "... my family has lived in constant fear and under death threats.
"I live in hiding with my five children as near as possible to Asia. She needs us very much to help keep her alive, to bring her medicine and good food when she is sick.
"After my wife had spent four long years in prison in terrible conditions, we were hoping that the high court of Lahore would free my wife.
"She did not commit blasphemy, never.
"We do not understand why our country, our beloved Pakistan, is so against us.
"We are Christians but we respect Islam. Our neighbours are Muslims and we have always lived well with them in our little village.
"We are convinced that Aasia will only be saved from being hanged if the venerable President Mammon Hussain grants her a pardon.
"My five children and I have only survived thanks to the protection of a few faithful friends who risk their lives daily to help us.
"Hearing that people are supporting Asia from so far away is so important for us. It helps us to hold on."