This image, sent in by 12-year-old patient Stewart Mackay, shows many people are ignoring the no-smoking message and dodging wardens at Yorkhill Hospital.
The youngster said he was "shocked" to see so many cigarette ends in the hospital grounds.
He said: "I have been going to Yorkhill for many years and for the whole time the amount of cigarettes outside Yorkhill has risen and risen I was there on Friday, September 6, and I took this picture.
"I am shocked at how many cigarettes are outside a children's hospital and no-one can sweep them up or have a bin to put them in."
The health board has rebranded entrances outside all of the city's hospitals with bold no smoking signs and wardens patrolling sites.
Young patients from Yorkhill created artwork to help get the message across.
NHS Greater Glasgow and Clyde said the ban had led to a significant reduction in the number of smokers outside hospital entrances but admitted that "changing deep rooted behaviours" would take time.
Three wardens at Gartnavel hospital quit their jobs after only a week in post due to verbal abuse from smokers. The health board said they were replaced within a week.
A spokeswoman for NHSGGC said: "We absolutely agree with Stewart that discarded cigarette ends thrown onto the ground within hospital sites is very unpleasant.
"Our zero tolerance to smoking on hospital grounds campaign has already resulted in a significant reduction in the number of smokers at hospital entrances where we have created giant red hatched zones, backed up by rebranded doors and windows and smoking wardens on patrol to make it clear that smoking is forbidden.
"However, we do know that changing deep-rooted behaviours in a hard core of smokers will take time.
"Facilities staff do work to clear used cigarette ends, however we do not provide cigarette bins as our acute hospital sites are completely no smoking, so to provide areas to smoke or to put out cigarettes would contradict this zero tolerance message."