Despite appeals against his sentence the 52-year-old Akmal Shaikh is scheduled to be executed next week.
He was arrested two years ago in the north-western Chinese city of Urumqi, in possession of four kilos of heroin.
Shaikh is said to suffer from a bipolar disorder.
The United Kingdom's Prime Minister Gordon Brown has asked the Chinese authorities to spare Shaikh.
The international human rights organisation Reprieve said, "It has evidence he was tricked into smuggling the drugs by a criminal gang."
Reprive further said, "If the death penalty is carried out Shaikh would become the first national from a European Union country to be executed in China in 50 years."