China accounts for nearly three quarters of the world's executions every year, according to human rights campaigners.
Figures from Amnesty International show a minimum of 7,000 death sentences were handed down in China in 2008, with 1,700 executions taking place.
Amnesty International said the Chinese authorities refused to make public national statistics on death sentences and executions and the real figure was "undoubtedly higher".
Steve Ballinger, a spokesman for Amnesty International, said: "China accounts for 72% of the world's executions and China executes far more than any other country by an awfully long way."
Under Chinese criminal law, a mental patient who commits a crime, and has not completely lost the ability to recognise or control his own conduct at the time, still has criminal responsibility but may be given a lighter punishment.
Mr Ballinger said Amnesty, which campaigns against the use of the death penalty, was concerned that trials in China fall below international fair trial standards.
He said Akmal Shaikh was "very unlikely" to have received a fair trial.
Other areas of concern to Amnesty in China include restrictions on freedom of expression, and the frequent use of torture in custody - although he said there was no evidence that Shaikh had suffered this.
Although there was still a "long way to go", he said there had been some gradual improvement, with China earlier this year stating that the Supreme People's Court had to review all death penalty cases.
According to Amnesty International, the Chinese authorities stated their intention in 2008 to increase the use of lethal injection as a "more humane" method of execution than firing squad.
The organisation said China voted in December 2008 against a UN General Assembly resolution calling for a worldwide moratorium on executions.