Kiaran Stapleton,21, pleaded guilty to manslaughter on the grounds of diminished responsibilty but denied murder when he appeared at Manchester Crown Court.
His " mad not bad " defence of diminished responsibility was not accepted by the prosecutor Brian Cummings QC and Stapleton will face a murder trial on June 25.
Stapleton,dressed in grey jogging top and bottoms, made a 20 minute appearance yesterday before Mr Justice Henriques at a plea and case management hearing.
The judge said:"The defendant has admitted the killing and the trial will be whether he was of diminished responsibility.It is plainly now within public knowledge that this was a shooting at very close range of a complete stranger."
Stapleton, who is represented by Mr Simon Czoka QC, was remanded in custody until the trial at Manchester Crown Court.
Student Anuj Bidve,23, had arrived in the UK from his home town of Pune in India in September 2011 to study on a micro electronics course at Lancaster University.
He died on a Christmas break and shopping trip to Manchester when he walked with friends through the Ordsall area of Salford in the early hours of Boxing Day on their way to the sales.
His father Subhash , who runs an air condioning firm, and mother Yogini, who runs her own business logisitics company, flew from their home in Pune for yesterday's hearing.
They were led into the court by police officers but were blocked from Stapleton's view by the dock, which was screened by opaque glass.
Mr Bidve, dressed in a grey suit, white shirt and pink tie, and his wife, in traditional Indian dress, listened intently to the proceedings but showed no emotion.
In a statement issued after the case,the couple said:"We have made the journey from India to the United Kingdom because it was very important to us to hear, in person, Kiaran Stapleton's plea.
"This is the first time we have returned to the UK since Anuj was taken away from us on Boxing Day last year and the first time we have come face to face with the man charged with his murder. So clearly this is a very emotional time and difficult time for us.
"We have today heard in person that Kiaran Stapleton has admitted killing Anuj. We know that there is a tremendous amount of interest both at home in India and here in the United Kingdom.
"As there will be a trial later this month, we cannot say anything further at this time and we would ask that the media respect both our privacy and the integrity of the court process.
"At the conclusion of the case, we will be happy to speak to the media. Thank you."