Donna Mayley told the BBC that existing sentences did not act as a deterrent.
Her son, Dean, 24, who suffered from learning difficulties, was murdered during a mugging in February last year.
It comes as latest crime figures show knife possession offences in England and Wales have risen to the highest level in three years.
More than 17,000 offences were recorded in 2014-15 while there were more than 13,000 stabbings and knife attacks in the year to June 2015, up 15% on the previous year.
Mrs Mayley said: "Nothing's going to deter these kids. They think it's normal, like having a wallet. It's just unbelievable that the courts just keep letting them get away with it."
She added: "The courts have got to change.... When it comes to knife crime they can't let them go.
"When they're stopped and caught with a knife they've got to be sent to prison. "
Dean Mayley was stabbed in the heart as he walked along Ruislip Road in Greenford, on 7 February 2014.
He was on his way to visit his uncle when he was attacked by four teenagers who confronted him in the street and stabbed him as they tried to rob him.
Jamal Jones, 17, from Acton, who wielded the knife, was convicted of murder and jailed for life, to serve a minimum of 15 years.
Michael Mensah, 18, Ryan Beresford, 19, and Miguel Leiba, also 17, were all jailed for manslaughter and attempted robbery.
Knife crime has resulted in the death of 15 teenagers in London since January, while last week a man was charged after stabbing a number of people at Leytonstone tube station.
The ONS said the rise in knife attacks represented "a real change in the downward trend seen in recent years".
In October, Metropolitan police commissioner Sir Bernard Hogan-Howe said rising recorded knife crime had led the force to increase the use of stop and search in the majority of London's 32 boroughs and had started to use powers allowing stops without reasonable suspicion.
In June he told the BBC: "Over the last three months there has been a rise in stabbings and that has caused us to review our position on stop and search???. If we are getting to the stage where people think they can carry knives with impunity, that can't be good for anyone."
But Home Secretary Theresa May has criticised the approach, saying there is no link between a rise in violence and a decline in the use of stop and search.
The mother of a young man who was stabbed to death in west London has pleaded with judges to impose jail terms on anyone caught with a knife.