Vinay Sharma, among the four men sentenced to death for the crime, tried to hang himself with a towel inside his cell in Delhi's high-security Tihar jail on Wednesday night, prison spokesman Bijender Kumar said.
"Security personnel in jail premises rescued the man and he was admitted to a nearby government hospital around midnight," Kumar said.
The fatal gang rape of the 23-year-old medical student on a Delhi bus in December 2012 drew mass protests and an international outcry that led to tougher anti-rape laws in the country.
In March 2013, another convict, Ram Singh, the driver of the bus in which the woman was assaulted, was found hanging in the Tihar jail.
Sharma lawyer AP Singh said his client had demanded more security, alleging he had been beaten by other inmates.
"Vinay recently complained about being tortured by inmates inside jail. It is not a suicide attempt but an attempted murder," he said.
The convicts were handed death penalties by a trial court in September 2013, which was confirmed by the Delhi High Court in 2014. They have challenged the verdict and their appeals are being heard by the Supreme Court.
