Thornwood Out of School Service was given a '2' rating for care during a snap inspection, the second lowest grade that can be awarded.
Inspectors found a volunteer had been taken on to help with children during busy periods but there was no evidence that any background checks had been carried out.
The report, by the Care Inspectorate, also identified a number of safety hazards with the centre's medication policy.
It did not make it clear who was responsible for administering medicine to pupils.
The report states: "It was clear that staff did not have consent for named medication for children."
Thornwood Out of School Service shares an address with Thornwood Primary, on Thornwood Avenue, but is not run by Glasgow City Council.
Inspectors found that during one outing the manager failed to carry out a risk assessment and told inspectors it had been done "in her head".
The service, which caters for a maximum of 32 children, was also rated weak for staffing and environment and unsatisfactory for management during the inspection on January 21.
None of the eight requirements from previous inspections had been dealt with to a satisfactory level.
The service has been told to improve safety procedures and to ensure that evidence is provided of safety checks carried out on staff.
The Care Inspectorate said the service manager would require support and training, "to enable standards to be raised".
A Care Inspectorate spokesman said: "We have graded the quality of care being provided as '2' weak.
"We continue to have concerns about the quality of care being provided and are working closely with this service to ensure it improves.
"We have informed the service of the areas which require improvement, and have told the service what it must do to improve. This includes ensuring that children's health and welfare needs are met.
"It also includes ensuring that clear and effective systems are in place to safeguard children in relation to any medication that could be administered to them.
"We also require the service to provide evidence that the appropriate checks have been carried out on the suitability of staff to work with children.
"The safety and welfare of children is always our first priority."
No one from Thornwood Out of School Service was available for comment.