Employees at the Royal Infirmary were spotted smoking in uniform at an underpass near Alexandra Parade and at other sites around the hospital.
The NHS has a strict no-smoking policy and say staff are "prohibited from smoking" in their uniforms; a rule ignored by employees.
The underpass is regularly used by patients and visitors who are forced to walk through clouds of "toxic fumes" to reach the hospital.
Elaine Gallagher, a carer from Stepps, uses the Alexandra Parade underpass when she takes her stepfather, who has lung disease, to appointments.
The 46-year-old, who visits the city centre site every six weeks, said she is "sick" of walking through the smoke.
She is concerned for the health of her stepfather and other ill patients, and is calling for designated zones further away from the building.
Elaine said: "It was atrocious to have to walk through dozens of people -it was predominantly staff members - standing in such close proximity to the hospital.
"My stepdad uses oxygen which shouldn't be near smoke or flames either.
"People who are really ill are having to come out of the hospital and into that and it's just not acceptable."
On her last visit at the end of June, Elaine said "at least two dozen staff members", wearing green uniforms, were standing at the underpass.
She has also seen staff smoking "at every entrance" on other occasions.
She said: "The remainder of what they had smoked was all over the ground as well.
"It's bad enough that they are smoking but they don't even put it in the bin afterwards."
An NHS spokeswoman said staff are only allowed to smoke during meal breaks outwith hospital grounds, not on paid breaks, and only if "they were not in their uniform or wearing their ID badge".
She added: "Staff are not permitted to smoke while in uniform or anything identifying them as an NHSGGC member of staff.
"It would appear that this took place outwith our hospital grounds however we would speak to any individuals who have breached this policy.
"If any member of staff continues to breach our policy and smoke within our grounds, or smoke while in uniform or anything identifying them as an NHSGGC member of staff, they would be subject to the normal disciplinary procedures.
"Help is available to support staff who are smokers to quit, or at least seek support to help remain smokefree during the day while at work on healthcare grounds."