Over 220,000 have signed a petition to make the production, sale and use of cannabis legal.
The pros and cons of legalising cannabis was debated recently in the House of Commons.
Anne McLaughlin SNP MP for Glasgow North East says she has been told the biggest support for legalisation came from Glasgow.
She has called for more research into the effects of cannabis as she has heard from many constituents on both sides of the argument.
She said: “The health effects of cannabis at a societal level, its relation to other drugs including tobacco and its relationship, causal or otherwise, with mental health problems require further study.”
She said she did not envy those who had to decide on the matter and noted a “fragmented” approach within the UK with Westminster responsible for the control of drugs but Holyrood for the treatment and prevention of drug problems.
The petition states: “Legalising cannabis could bring in £900m in taxes every year, save £400m on policing cannabis and create over 10,000 new jobs.”
Across Glasgow more than 3000 people signed up with Glasgow Central the highest number with 539 Glasgow East had 487 and Glasgow North East 449.
“A substance that is safer than alcohol, and has many uses. It is believed to have been used by humans for over 4000 years, being made illegal in the UK in 1925.”
The UK Government response to the petition states: “We must prevent drug use in our communities; help dependent individuals through treatment and wider recovery support; while ensuring law enforcement protects society by stopping the supply and tackling the organised crime that is associated with the drugs trade.”